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A176494 Least m >= 1 for which |2^m - prime(n)| is prime. 1
3, 1, 1, 2, 1, 2, 1, 2, 4, 1, 3, 2, 1, 2, 4, 4, 1, 3, 2, 1, 3, 2, 4, 3, 2, 1, 2, 1, 2, 47, 2, 6, 1, 8, 1, 3, 5, 2, 4, 4, 1, 6, 1, 2, 1, 5, 5, 2, 1, 2, 4, 1, 8, 4, 6, 8, 1, 3, 2, 1, 4, 7, 2, 1, 2, 9, 791, 4, 1, 2, 8, 3, 9, 5, 2, 4, 3, 2, 3, 8, 1, 6, 1, 3, 2, 4, 3, 2, 1, 2, 4, 3, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n)=1 iff p_n is second of twin primes (A006512); for n > 4, a(n)=2 iff p_n is second of cousin primes (A046132). It is interesting to continue this sequence in order to find big jumps such as a(31)-a(30). Is it true that such jumps can be arbitrarily large, either (a) in the sense of differences a(n+1)-a(n), or (b) in the sense of ratios a(n+1)/a(n)?

Conjecture. For every odd prime p, the sequence {|2^n - p|} contains at least one prime. The record values of the sequence appear at n = 2, 10, 31, 68, 341, ... and are 3, 4, 47, 791, ... Note that up to now the value a(341) is not known. Charles R Greathouse IV calculated the following two values: a(815)=16464, a(591)=58091 and noted that a(341) is much larger [private communication, May 27 2010]. - Vladimir Shevelev, May 29 2010

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..340

MATHEMATICA

lm[n_]:=Module[{m=1}, While[!PrimeQ[Abs[2^m-n]], m++]; m]; Table[lm[i], {i, Prime[ Range[2, 100]]}] (* Harvey P. Dale, Aug 11 2014 *)

CROSSREFS

Cf. A176303, A175347, A006512, A046132.

Sequence in context: A258820 A030347 A010275 * A157229 A242248 A107297

Adjacent sequences: A176491 A176492 A176493 * A176495 A176496 A176497

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Apr 19 2010, Aug 15 2010

EXTENSIONS

Beginning with a(31), the terms were calculated by Zak Seidov - private communication, Apr 20 2010

Sequence extended by R. J. Mathar via the Seqfan Discussion List, Aug 15 2010

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)