Mark Gritter (markgritter) wrote,
Mark Gritter
markgritter

Integer sequence puzzle

The week a co-worker brought in a puzzle her child had been assigned in math class. The beginning and end of the sequence were given as 4 and 134. I offhandedly remarked that I would just cheat using the Online Encyclopedia of Integer Sequences.

By now, of course, I've forgotten how many entries there were in the sequence! There were at least 4. Can I still use the OEIS to identify it?

4, _, _, _, _, 134:

4, 6, 26, 34, 86, 134, ... are "interprimes which are of the form 2*prime". (A075277) An interprime is the mean of two consecutive primes.

A047732 and A056309 are good candidates too but they have prefixes.

4, _, _, _, _, _, 134:

Some interesting candidates but none without a prefix.

4, _, _, _, _, _, _, 134:

4, 26, 28, 52, 76, 98, 124, 134, ... are "middle side of the first primitive d-arithmetic triangle" (A047732) which I am unable to decipher.

I particularly like the Moebius Transform of Fibonacci numbers 1, 0, 1, 2, 4, 6, 12, 18, 32, 50, 88, 134. A007436.

4, _, _, _, _, _, _, _, 134:

4, 7, 40, 49, 59, 70, 85, 125, 134, ...: numbers n such that n^12 reversed is prime! Obviously A059213 is what was desired, it's so obvious!

4, 9, 15, 26, 39, 58, 85, 111, 134, ... are "semiprimes with triangular indices" (A122964) which is also cool.

4, _, _, _, _, _, _, _, _, 134:

4, 14, 34, 38, 40, 56, 80, 110, 128, 134, ...(A032645) are numbers n such that n concatenated with n+5 is a lucky number.

4, 5, 7, 8, 9, 13, 15, 52, 82, 134, ... (A119642) are indices of prime numbers of trees with n unlabeled nodes, which is neat but not a "basic" sequence.

... and we seem to be getting more candidates with bigger gaps. Alas, none of these look like an appropriate grade-school "trick" question.
Tags: geek, math, puzzles
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