Which number comes next? Ask the Encyclopedia of Integer Sequences.
The OEIS sits long on sequences that tease and land as a joke – like the eban sequence, invented by Dr. Sloane. “It’s very, very simple,” he said. “And yet no one ever guesses.”
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 …
The point of the eban numbers is that the letter “e” is forbidden: this sequence does not contain digits that, when spelled out, contain the letter “e”.
“Eban kind of sounds like ‘even’ and it’s a really nice play on words,” said Dr. Sloane – because if you look at numbers without an “e”, they’re all even. “This is an old theorem of mine: that every odd number contains an ‘e’, in English. And so all numbers where ‘e’ is forbidden are even. Of course, not all even numbers are eban, but enough to make a good sequence.”
What’s the next number?
Here are a few more ranges to try (answers below):
1) 0, 1, 8, 11, 69, 88, 96, 101…
2) 1, 11, 21, 1211, 111221, 312211…
3) 5, 8, 12, 18, 24, 30, 36, 42…
4) 14, 18, 23, 28, 34, 42, 50…
Dr. Sloane first started looking for a sequence in 1964, as a graduate student. By studying pathways in an artificial neural network (a mathematical system that mimics the human brain), his calculations generated:
0, 1, 8, 78, 944, 13800 …
“I desperately needed a formula for the nth term to determine the growth rate of the terms,” he wrote in a retrospective published in April. “This would indicate how long activity would persist in this very simple neural network.” Chasing textbooks, reference books, magazines, he got close, but no order. Ultimately, along with the combinatorial John Riordan, he picked the formula and the following term: 237432.