

A176494


Least m>=1 for which 2^mp_n is prime, where p_n is the nth 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 arbitrary 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^np} contains at least one prime. The records of the sequence appear in points 2,10,31,68,341,... and equal to 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 at 27.05.10. [From 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. The sequence was extended by R. J. Mathar via the Seqfan Discussion List (Aug 15 2010).


STATUS

approved



