Interesting or Inspiring Sequences 2018 HW1

(1)

2018 HW1

Interesting or Inspiring Sequences

(2)

NUMBER

(3)

Hw1 An interesting sequence r06922114 陳啟元 The sequence : 1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, …

which is defined by a(n+1) = a(n) + (the product of the nonzero digits of a(n)). (e.g. 74 = 62 + 6 * 2)

Why it’s interesting? : There is a theory by Paul Loomis states that starting from any positive integer, its sequence will join the sequence started from 1.

(e.g. 3, 6, 12, 14, 18, 26, 38, 62, 74, 102, ...)

(4)

Digit Product Sequence

R07922054 駱定暄

•

^{初始條件：從正數開始}

•

數列遞迴規則：後一項數字為前一項數字非零位的乘積，加上前一項數字本身。 ex. 102 的下一項為 (1*2)+102=104

•

舉例，從 1 開始： 1, 2, 4, 8, 16, 22, 26, 38, 62, 74, …

•

有趣的事情是，所有正數起始的數列，最後都會與從 1 開始的數列重合，比方說，從 3 開始的數列，會在 26 與從 1 開始的數列重合

•

^{參考資料：}

^https

://facstaff.bloomu.edu/ploomis/sequences.html

(5)

Florian Heemeyer | Algorithms for Biological Sequence Analysis | Homework 1

5

Florian Heemeyer (A07945101)

Morris Number Sequence

1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211 …..

Explantation:

This sequence grows indefinitely but contains just the digits 1, 2 and 3.

n Previous value Value n

1 - 1

2 “One one” 11

3 “Two ones” 21

4 “One two & one one” 1211

(6)

Keming Kao T07902108

On the right is an interesting application of the Fibonacci sequence: When male bees are born, the egg is unfertilized, so there is only 1 parent. When female bees are born, the egg is

fertilized, so they have 2 parents. After a few generations, we see that each one corresponds to sequential Fibonacci numbers!

Credit: Internet

(7)

HW#1 Perfect Numbers Sequence

• The sequence: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328 …

• The sequence I want to introduce is perfect numbers.

• The perfect numbers have some special properties.

• 1.The perfect number is equal to the sum of all of its factors.

• for example:

• factors of 6: 1, 2, 3. 6 = 1 + 2 + 3

• factors of 28: 1, 2, 4, 7, 14, 28 = 1 + 2 + 4 + 7 + 14

• 2.Perfect numbers (even perfect numbers) are all ended with ”6” or “28”.

• 3. They can be the sum of “consecutive integers”

• for example:

• 6=1+2+3

28=1+2+3+4+5+6+7 496=1+2+3+…+30+31

R06945028 陳胤竹

(8)

D07945011 江尚瑀

It has three kinds way to find the answer.

Source: Internethttps://www.ettoday.net/news/20170608/940920.htm

The answer is 6. The answer is 9. The answer is 14.

(9)

R07922061 陳力

•1, 1, 2, 5, 14, 42, 132, 429…

•Reason:

•Corresponds to counting of many combinatori al objects

•Binary trees, bracket sequences…

Catalan numbers oeis.org/A000108

(10)

Interesting Sequence HW1

• ^381654729

• 此數前 n 項組成的數字會被 n 整除恰好是 1~9 不重複數字組成，且唯一

• 設數字為 abcdefghi ，偶數位置必須被 2 整除 b, d, f, h 為偶數

e 必定為 5 ， cd 為 4 的倍數， fgh 為 8 的倍數 (gh 為 8 的倍數 )

abc, def, ghi 為 3 的倍數， efg-bcd+a 為 7 的倍數

• R06922026 柯東爵

Ref: http://www.mathland.idv.tw/fun/divndigit.htm

(11)

INTERESTING SEQUENCE : 142857

REASON WHY IT IS INTERESTING

 142857 * 1 = 142857

 142857 * 2 = 285714

 142857 * 3 = 428517

 142857 * 4 = 571428

 142857 * 5 = 714285

 142857 * 6 = 857142

 142857 * 7 = 999999

 142 + 857 = 999

 14 + 28 + 57 = 99

 142857 * 142857 = 20408122449, 20408 + 122449 = 142857

B05303003 資工三黃奎鈞

(12)

Hexagonal Numbers

• An hexagonal number or hexagon number counts the objects that can form an equilateral hexagon. The nth hexagon number is the number of dots or balls in an hexagon with n dots on a side:

• The formula for the nth hexagonal number:

• The first few hexagonal numbers are:

• 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231…

Marya Rezzouk, [ID:A07922202]

(13)

Hw1

• Name ：吳孟軒

• Sequence ：

0, 1, 2, 5, 6, 10, 11, 13, 15, 17, 23, 25, 27, 32, 33, 35, 41, 49, 52, 55, 57, 59, 62, 65,

67, 69, 71, 83, 86, 91, 95, 99, 110, 125, 132, 140, 150, 159, 160, 165, 168, 174, 178, 181, 189, 192, 198, 2 07, 211, 220, 229, 230, 235, 240, 243, 250, 257, 264, 270, 272, 284, 288, 299, 303, 311, 315, 319, 324, 327, 3 30, 335, 338, 342, 349, 356, 362, 367, 369, 370, 371, 372, 373, 374

• 這個序列是高速公路交流道公里數。小時候常常往返家與阿嬤家，在車上無聊就把一些交流道的公里數與交流道數字記起來了，於是對這些里程數很熟悉！但是現在交流道沒專屬數字，只剩下公里數，

也是少了一些童年回憶。

(14)

[HW1] Freemasonry cipher

• Student ID : r07922153

• Name : Sakura Yamaki(八巻櫻 )

• Interesting sequence is as follow.

6288 1918 2237 130002 6289 1945 2166 100221 6290 1789 2226 1111111

• Reference : https://tocana.jp/2018/06/post_17327_entry_2.html

• Explanation :

• Just on the morning of June 25^th 2018, the official Twitter account of Freemason Japan Grand Lodge tweeted a strange sequence that seems to be cipher as describ ed above.

• And this cipher has not been solved yet, so I think that it’s interesting!

(15)

POEM

(16)

趣言能適意，茶品可清心。

心清可品茶，意適能言趣。

• 這首詩不只有回文格式，念起來亦順暢帶有閒趣。

• B04902064 李衡

(17)

B04902084 王建元

王安石的回文詩【碧蕪】

碧蕪平野曠，黃菊晚村深；

客倦留甘飲，身閑累苦吟。

倒讀成：

吟苦累閑身，飲甘留倦客；

深村晚菊黃，曠野平蕪碧。

有趣的地方是無論正讀還是反讀，詩裡疲倦愁苦的意境都不變，而且仍然充滿詩意。

(18)

英文回文詩

資工所 R07922117 黃榆珊

• 這是一首英文回文詩，可以從開頭往下讀，也可以從結尾一行一行倒回讀。之前比較常見到中文的回文詩，英文回文詩受限於語言的關係，比較少能一字一字倒回來讀，但一句一句倒回來唸倒是可以。

• 選這首詩的原因是因為覺得有被這首詩激勵到，由上往下讀時能夠感覺到整首詩充滿了自卑的想法，覺得自己不夠好、不會受人喜愛。但由下往上讀回時，整首詩充滿了樂觀與自信，作者似乎是想傳達「你是美麗、有價值的人」的想法給讀者。這首詩似乎也是在提醒我們：你決定如何讀這首詩就代表你怎麼看待自己。

Source:

https://www.sunnyskyz.com/blog/2515/There-Are- 2-Ways-To-Read-This-Poem-The-One-You-Choose- Will-Be-The-Difference-In-Your-Life

(19)

聯珠迴文詩

《春》鶯啼岸柳弄春晴，

柳弄春晴夜月明。

明月夜晴春弄柳，

晴春弄柳岸啼鶯。

《夏》香蓮碧水動風涼，

水動風涼夏日長。

長日夏涼風動水，

涼風動水碧蓮香。

《秋》秋江楚雁宿沙洲，

雁宿沙洲淺水流。

流水淺洲沙宿雁，

洲沙宿雁楚江秋。

《冬》紅爐透炭炙寒風，

炭炙寒風御隆冬。

冬隆御風寒炙炭，

風寒炙炭透爐紅。

聯珠迴文詩是因詞語相互套結而得名，其為七言絕句的延伸變革，句型字數以四、三配對。清代吳絳雪的《春夏秋冬》乍看會讓人百思不得其解，但是每一句都可以用廻文自成一首七言絕句，分別描寫春、

夏、秋、冬的景色。

讀法：以一至七字為首句，四至十字為承句，然後倒句回讀之，為轉句及末句。

範例： X¹ X² X³ X⁴ X⁵ X⁶ X⁷ X⁸ X⁹ X¹⁰

❶ ❷

❹ ❸

《春夏秋冬》

清吳絳雪•

鶯啼岸柳弄春晴夜月明香蓮碧水動風涼夏日長秋江楚雁宿沙洲淺水流紅爐透炭炙寒風御隆冬

D04945013 生醫電資所博四游文萱

(20)

賴達資工四 b04902034

四字詞性相同之四字成語可隨意排序，意義不變

● 名詞類 : 琴棋書畫、絲竹管弦、金石絲竹、規矩繩墨、禮義廉恥、風雲月露、

東西南北、樓台亭閣、王侯將相

● 動詞類 : 捭闔縱橫、起承轉合、望聞問切、嬉笑怒罵、賞罰黜陟、洗削更革、

切磋琢磨、打滾撒潑、挑撥離間

● 形容詞 : 悲歡離合、輕重緩急、溫柔敦厚、喜怒哀樂、隱晦曲折、清新俊逸、

豐亨豫大、光明磊落、忠孝節義

● 參考連結

(21)

• 古之欲明明德於天下者，先治其國；欲治其國者，先齊其家；欲齊其家者，先修其身；欲修其身者，先正其心；欲正其心者，先誠其意；欲誠其意者，先致其知；致知在格物。

• 物格而后知至，知至而后意誠，意誠而后心正，心正而后身修，身修而后家齊，家齊而后國治，國治而后天下平。

 以前背大學的時候就覺得這段很有趣，前面的遞升和後面的遞降相互乎應，又字詞前後順序互換還是相同的意思，

實在覺得中文非常奧妙！

分醫所碩二周毓慈 P06448007

(22)

• 六十老兒生一子人言非是我子也家產田園盡付與女婿外人不得爭執。

• 六十老兒生一子，人言：『非是我子也！』家產田園盡付與女婿

，外人不得爭執。

• 六十老兒生一子，人言非，是我子也！家產田園盡付與。女婿外人，不得爭執。

D07943002 陳彥龍

(23)

HW1. an interesting sequence

• Acrostic word for Father’s day in English

FUN

HANDSOME INTELLIGENT HAPPY

HERO GREAT

Kai-Pu Chen, D04945020, BEBI

I think the sequence is interesting because there is a new hiding

meaningfully vocabulary (FATHER) in lots of words.

Especially, it can represent for Happy Father’s Day to admire that father is a fun, handsome, intelligent, happy, a hero and great man in the world! And it’s like Chinese poem called 藏頭詩 !

I think the sequence is interesting because there is a new hiding

meaningfully vocabulary (FATHER) in lots of words.

Especially, it can represent for Happy Father’s Day to admire that father is a fun, handsome, intelligent, happy, a hero and great man in the world! And it’s like Chinese poem called 藏頭詩 !

Reference: https://www.pinterest.com/pin/86412886572984901/

(24)

R07922080 資工碩一于建民

Janet was quite ill one day.

Febrile trouble came her way.

Martyr-like, she lay in bed;

Aproned nurses softly sped.

Maybe, said the leech judicial Junket would be beneficial.

Juleps, too, though freely tried, August ill, for Janet died.

Sepulchre was sadly made.

Octaves pealed and prayers were said .

Novices with ma'y a tear Decorated Janet's bier.

Source: https://zh.wikipedia.org/wiki/%E9%9B%A2%E5%90%88%E8%A9%A9 At first sight it looks like an ordinary story.

But after careful examination, one can find out that there’s some special hidden patterns: the initial three letters of each line are the abbreviations for twelve months! This is also called an “acrostic poem”. I find this kind of sequences quite interesting because there may be some information hidden behind the words other than their literal meanings.

(25)

A SEQUENCE WHICH IS SORT OF INTE RESTING OR INSPIRING.

There is a “lie” in believ e,

“over” in lover,

“end” in friend,

“us” in trust,

“ex” in next,

and “if” in life.

At first, I was looking for the sent ence “Even believe has a lie in it.

” but after searching on Google, I found the whole sentence.

It reminds people to be cautious and nothing is forever. It is interestin g of the “words” and inspiring of the meaning.

生醫電資碩二 r06945027 鍾明軒

(26)

Led Zepplin's Stairway to Heaven

• 歌詞片段

If there's a bustle in your hedgerow Don't be alarmed now

It's just a spring clean for the May queen Yes, there are two paths you can go by But in the long run

There's still time to change the road yo u're on

• 倒轉播放的結果

Oh, here's to my sweet Satan

The one whose little path would make me sad whose power is Satan

He'll give, he'll give you 666

There was a little toolshed where he made us suffer, sad Satan

R06922042 藍祥予

• 其中一段歌詞經過倒轉播放，竟然變成了撒旦崇拜的內容。

• 解說影片： https://youtu.be/IXpEtF4i1oI

• 參考資料： https://en.wikipedia.org/wiki/Stairway_to_Heaven https://en.wikipedia.org/wiki/Backmasking

(27)

BUSY

Being Under Satan's Yoke

Being a Christian, this acronym is frequently used as a reminder that Satan separates a man from God by making him busy. Matthew 11:29 wrote:

Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls. For my yoke is easy and my burden is light.

He thus has called us to take his yoke, which gives us peace, provided that we first relieve ourselves from our own yoke of

busyness. _R07922039_陳耘志

(28)

童年諺語歌謠

• 剪刀石頭布，你沒穿內褲，內褲夾在聯絡簿，送給老師當禮物，老師看了很生氣，一腳踢到美國去，美國小姐真美麗，送你一盒巧克力，邊走邊吃邊放屁，

阿里巴巴打屁屁

• 小姐小姐別生氣，明天帶妳去看戲，看什麼戲？

看妳爸爸流鼻涕，剃剃剃光頭，投投投大海，海海海龍王，王王王八蛋，盪盪盪鞦韆，牽牽牽牛花，花花花公子，子子你是我的乖孫子

 回想起小時候一些廣為人知但不太入流的順口溜，之所以能讓人琅琅上口，就是因為每一句的尾巴跟下一句的開頭相同，如同古文中的頂真修辭法。若將歌謠的每一句看成一個序列，也能想像這些序列藉由相似或互補的首尾相連接，饒富趣味。

臨醫所博一劉士嶢 D07421006

來源 : 話說童年哼唱遊戲

(29)

OTHER

(30)

Interesting Sequence

There are some names of diseases that contains certain irony wh ich I found very amusing. For example:

1. Hippopotomonstrosesquippedaliophobia: As one of the long est word in the dictionary, it means the fear of long words.

2. Aibohphobia: Different from the previous phobia, this word -- the fear of palindromes -- is probably more of a joke than act ual disease. However, it is still interesting since the word itsel f is a palindrome sequence.

B04902022 陳譽穆

(31)

[HW1] b03902125

林映廷

uvuvwevwevwe onyetenyevwe ugwemubwem ossas

I think it’s interesting because the name of certain African is funny, lengthy, and not easy to remember. You can see following two vedios to understand my

punch line. His parents’ name is so, too.

vedio 1 : https://www.youtube.com/watch?v=efmtZ1-qtt0 vedio 2 : https://www.youtube.com/watch?v=_q3b6wqXC6U

(32)

It is a tattoo that I designed for myself. It has the initials of my mother (G) and father (B). Interesting fact:

- The letters are same even when we see upside down.

- When seen from upside, G seems bigger than B. While from the opposite side, B is larger than G. This means sometimes I listen to my dad’s opinion and sometimes my mom’s opinion. But in both the cases I have the

blessings of both.

- The love symbol signifies their eternal love for each other and our family.

- Note that the loops of G and B make a kind of infinite symbol . This signifies my love for both of them forever.

Upside Downside

Source: Own imagination  Student ID: D07945014

(33)

(34)

Alphabetical Sequence

The skill required to be able to do this is amazing. I certainly couldn’t do it.

(35)

Adenosine Deaminase (ADA) Deficiency -

a missense mutation in the adenosine deaminase enzyme

Explanation: Mutations of the protein sequence of ADA are highlighted in yellow

[HW1] A07922108 Fabian Krauthausen

The Adenosine Deaminase (ADA) Deficiency is caused by a mutation on

chromosome 20 on the gene which codes the ADA enzyme. As a result, people with this disorder can only produce non-working ADA enzymes.

 ADA is an enzyme and thereby also an protein playing an important part for the immune system of the human. This enzyme is mainly produced in cells of the immune system

 The ADA enzyme normally breaks down toxic substances which naturally form when the DNA is broken down in the cells, in particular converting adenosine to inosine

 By the ADA deficiency, this ADA enzyme is not working properly anymore and the toxic substances can build up in the cells of the immune system, killing these immune cells and affecting the immune system of the human

 As a consequence, various infections can arise and harmless bacteria can lead to severe sicknesses

And all of this through missense mutations representing point mutations in a specific sequence on a gene by a change in a single nucleotide, resulting in a codon which codes for a different amino acid and hence creates defect enzymes.

Source:

https://learn.genetics.utah.edu/content/disorders/singl egeneeg/

Source:

Analysis of missense mutations in adenosine deaminase using Pathogenic-Or-Not-Pipeline (PON-P), Sreevani Kotha, 2010

Interesting Sequence: Reason:

(36)

Sometimes you have to think outside the box.

Connect all nine points without letting the pen leave the paper, with four straight lines.

I like this one because it always reminds me to think outside the box. When I was younger,

a math teacher showed it to me and since then I always try to think about a problem from different perspectives. It also remindes me that there is a solution to (mostly) every problem, no matter how impossible it seems to be.

- Julia Pelzer, T07901105

(37)

陳主牧

B03705037

這個象形文字序列是：

朗格朗格Rongorongo

根據維基百科，這是一個至今還沒被破解的古代語言，出現在復活節島

，多撰寫在木板上，因被西方征服者銷毀而數量稀少。

每次仔細端詳朗格朗格的文字，便會感覺到一股濃烈、詭譎的神秘感。

扭曲著、彷彿肢體的奇特線條，有時還會令我莫名地不寒而慄。雖然不明白其中的意義，光是觀看這些奇特的圖形相當有趣。

(38)

Yoga sequences

Usually yoga poses can be done without any particular order but for Ashtanga yoga, the sequence does matter. As my yoga teacher always said,

“ You fail to proceed to the next pose simply because you haven’t mastered the current one. ”.

Picture below demonstrates two of my favorite sequences from Ashtanga yoga beginner series. We start all practice sessions with five repetitions of sun salutation (Surya Namaskara A) and always end with the finishing sequence.

Immersing myself in yoga practice makes me feel calm, peaceful, and

contented. R06945042 張

生醫電資二子涵

(39)

姓名 : 劉晏均學號 :R06945016

系所 : 生醫電資 Source: Classic Anime

A Circular Sequence (A way of honing your

mind)

(40)

Some math

11 3 3 5 5 7 7 ? 44

99 88

22

I found this – years ago – in an episode of simpsons and liked it very much since in this case intuition and a

good eye is all you need. Sebastian Gütgemann

(41)

z

D07945011 江尚瑀

中華文化傳承五千年，千變萬化的中國文字，

更是歷久不衰的藝術資產，瞭解中國文字之美

Source: Internet：中國文字之美

美麗的姑娘雄鷹翱翔長命百歲雄

孫悟空唐僧

Interesting or Inspiring Sequences 2018 HW1

2018 HW1