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%I #15 May 28 2024 15:01:39
%S 0,1,3,1,5,3,3,1,9,7,5,3,17,27,3,1,29,3,21,7,17,15,9,43,35,15,29,3,11,
%T 3,11,15,17,25,53,31,9,7,23,15,27,15,29,7,59,15,5,21,69,55,21,21,5,
%U 159,3,81,9,69,131,33,15,135,29,13,131,9,3,33,29,25,11,15,29,37,33,15,11,7,23
%N Distance from 2^n to the next prime.
%C Essentially the same as A013597. - T. D. Noe, Jul 17 2007
%C From _Jianing Song_, May 28 2024: (Start)
%C Not every odd number is present, as no term can be equal to a Sierpiński number (for example 78557); cf. A076336. See also A067760.
%C Conjecture: Every odd number which is not a Sierpiński number is a term. In other words, for every odd k which is not a Sierpiński number, there exists some n >= 1 such that 2^n + 1, 2^n + 3, ..., 2^n + (k-2) are all composite while 2^n + k is prime. (End)
%H T. D. Noe, <a href="/A092131/b092131.txt">Table of n, a(n) for n=1..5000</a>
%F a(n) = nextprime(2^n) - 2^n.
%F a(n) = A007920(A000079(n)). - _Michel Marcus_, Oct 19 2022
%e a(13)=17 because 2^13=8192 and the next prime is 8209=8192+17.
%t Join[{0},NextPrime[#]-#&/@(2^Range[2,80])] (* _Harvey P. Dale_, Jun 06 2012 *)
%o (PARI) for(i=1,100,x=2^i;print1(nextprime(x)-x,","))
%Y Cf. A013597.
%Y Equivalent sequence for previous prime: A013603.
%Y Cf. A000079, A007920, A067760, A076336.
%K easy,nonn,changed
%O 1,3
%A Helmut Richter (richter(AT)lrz.de), Mar 30 2004
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