

A176494


Least m >= 1 for which 2^m  prime(n) is prime.


0



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
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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

Table of n, a(n) for n=2..95.


MATHEMATICA

lm[n_]:=Module[{m=1}, While[!PrimeQ[Abs[2^mn]], 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



