EBS Morning Special 5월 28일 일요일: What Number Comes Next?

1.  NEW YORK TIMES

What Number Comes Next? The Encyclopedia of Integer Sequences Knows.

Siobhan Roberts

c.2023 The New York Times Company

 

 

Some numbers are odd: 1, 3, 5, 7, 9, 11, 13, 15. Some are even: 2, 4, 6, 8, 10, 12, 14, 16. And then there are the puzzling “eban” numbers:  2, 4, 6, 30, 32, 34, 36, 40 and so on. What number comes next? And why?

 

[Expressions]

▶odd : 홀수의 

▶even : 짝수의 

 

 

 

These are questions that Neil Sloane, a mathematician of Highland Park, New Jersey, loves to ask. Sloane is the founder of the On-Line Encyclopedia of Integer Sequences, a database of 362,765 (and counting) number sequences defined by a precise rule or property. Such as the prime numbers, like 2, 3, 5, 7, 11, 13, 17, 19.

 

Or the Fibonacci numbers — every term (starting with the third term) is the sum of the two preceding numbers:  0, 1, 1, 2, 3, 5, 8, 13  and so on.

 

[Expressions]

▶Integer Sequences : 정수 수열   

integer 정수 

fraction : 분수  

improper fraction : 가분수  

▶A prime number : 소수 (a natural number greater than 1 that has no positive divisors other than 1 and itself.) – * 한글 발음 유의  

▶the sum of the two preceding numbers : 앞에 오는 2 숫자를 더한 값 

 - preceding : 이전의, 선행하는 

 

 

 

This year the OEIS, which has been praised as “the master index to mathematics” and “a mathematical equivalent to the FBI’s voluminous fingerprint files,” celebrates its 50th anniversary. The original collection, “A Handbook of Integer Sequences,” appeared in 1973 and contained 2,372 entries. In 1995, it became an “encyclopedia,” with 5,487 sequences and an additional author, Simon Plouffe, a mathematician in Quebec. A year later, the collection had doubled in size again, so Sloane put it on the internet.

 

“In a sense, every sequence is a puzzle,” Sloane said in a recent interview. He added that the puzzle aspect was incidental to the database’s main purpose: to organize all mathematical knowledge.

 

[Expressions]

▶be praised : 칭찬을 받다. 

▶celebrate its 50th anniversary : 50주년을 기념하다.  

▶double in size : 크기가 두 배가 되다. 

 

 

 

The OEIS is long on sequences that tease and land like a joke — like the eban sequence, invented by Sloane. “It’s very, very simple,” he said. “And yet nobody ever guesses it.”

 

More terms are not necessarily helpful: 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, 2000, 2002, 2004, 2006, 2030 and so on.

 

[Expressions]

▶tease : 놀리다, 못 살게 굴다.  

 

 

 

 

The punchline of the eban numbers is that the letter “e” is banned: This sequence contains no numbers that, when the numbers are spelled, contain the letter “e.”

 

“Eban sounds a bit like ‘even,’ and it’s a very nice pun,” Sloane said — because if you look at numbers without an “e,” they are all even. “This is an old theorem of mine: that every odd number has an ‘e’ in it, in English. And so all the numbers where ‘e’ is banned are even. Of course, not all even numbers are eban, but enough are to make a good sequence.”

 

[Expressions]

▶punchline : 농담에서 핵심이 되는 결정적인 구절 / 대목,  

▶the punchline of the eban numbers is : eban숫자에서의 핵심은~  

▶theorem : (수학에서의) 정리 

ex. Pythagoras’ theorem 피타고라스의 정리 

 

 

 

Here are a few to try. The answers are below.

 

A) 0, 1, 8, 11, 69, 88, 96, 101 …

 

B) 1, 11, 21, 1211, 111221, 312211 …

 

A) 111. These are the “strobogrammatic” numbers — the same upside-down, or rotated 180 degrees (not flipped along the horizontal axis).

 

B) 13112221. This is the “Look and Say” sequence: At the first term, 1, you describe what you see — one 1 — so the next term is 11. At the second term (11) you again describe what you see — two 1s — so the next term is 21. Describing that — one 2 and one 1 — results in the next term, 1211, and so on.

 

[Expressions]

▶upside-down : 거꾸로 뒤집다. 

▶rotate 180 degrees : 180도 뒤집다.

▶flipped along the horizontal axis : 가로축을 따라 뒤집은