A013597 - OEIS

A013597

a(n) = nextprime(2^n) - 2^n.

1, 1, 1, 3, 1, 5, 3, 3, 1, 9, 7, 5, 3, 17, 27, 3, 1, 29, 3, 21, 7, 17, 15, 9, 43, 35, 15, 29, 3, 11, 3, 11, 15, 17, 25, 53, 31, 9, 7, 23, 15, 27, 15, 29, 7, 59, 15, 5, 21, 69, 55, 21, 21, 5, 159, 3, 81, 9, 69, 131, 33, 15, 135, 29, 13, 131, 9, 3, 33, 29, 25, 11, 15, 29

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

A013597 and A092131 use different definitions of "nextprime(2)", namely A151800 vs A007918: A013597 assumes nextprime(2) = 3 = A151800(2), whereas A092131 assumes nextprime(2) = 2 = A007918(n). [Edited by M. F. Hasler, Sep 09 2015]

If (for n>0) a(n)=1, then n is a power of 2 and 2^n+1 is a Fermat prime. n=1,2,4,8,16 are probably the only indices with this property. - Franz Vrabec, Sep 27 2005

Conjecture: there are no Sierpiński numbers in the sequence. See A076336. - Thomas Ordowski, Aug 13 2017

LINKS

T. D. Noe, Table of n, a(n) for n = 0..5000

V. Danilov, Table for large n

FORMULA

a(n) = A151800(2^n) - 2^n = A013632(2^n). - R. J. Mathar, Nov 28 2016

Conjecture: a(n) < n^2/2 for n > 1. - Thomas Ordowski, Aug 13 2017

MAPLE

A013597 := proc(n)

nextprime(2^n)-2^n ;

end proc:

seq(A013597(n), n=0..40) ;