cp's OEIS Frontend

A013597 a(n) = nextprime(2^n) - 2^n.

%I A013597 #35 Dec 02 2024 18:10:56
%S A013597 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,
%T A013597 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,
%U A013597 159,3,81,9,69,131,33,15,135,29,13,131,9,3,33,29,25,11,15,29
%N A013597 a(n) = nextprime(2^n) - 2^n.
%C A013597 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]
%C A013597 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
%C A013597 Conjecture: there are no Sierpiński numbers in the sequence. See A076336. - _Thomas Ordowski_, Aug 13 2017
%H A013597 T. D. Noe, <a href="/A013597/b013597.txt">Table of n, a(n) for n = 0..5000</a>
%H A013597 V. Danilov, <a href="https://web.archive.org/web/20060127010153/http://www.fortunecity.com:80/skyscraper/epson/276/pr1_2k.htm">Table for large n</a>
%F A013597 a(n) = A151800(2^n) - 2^n = A013632(2^n). - _R. J. Mathar_, Nov 28 2016
%F A013597 Conjecture: a(n) < n^2/2 for n > 1. - _Thomas Ordowski_, Aug 13 2017
%p A013597 A013597 := proc(n)
%p A013597     nextprime(2^n)-2^n ;
%p A013597 end proc:
%p A013597 seq(A013597(n),n=0..40) ;
%t A013597 Table[NextPrime[#] - # &[2^n], {n, 0, 73}] (* _Michael De Vlieger_, Aug 15 2017 *)
%o A013597 (PARI) a(n) = nextprime(2^n+1) - 2^n; \\ _Michel Marcus_, Nov 06 2015
%o A013597 (Python)
%o A013597 from sympy import nextprime
%o A013597 def A013597(n): return nextprime(m:=1<<n)-m # _Chai Wah Wu_, Dec 02 2024
%Y A013597 Cf. A014210, A092131, A007918, A151800.
%K A013597 nonn
%O A013597 0,4
%A A013597 James Kilfiger (mapdn(AT)csv.warwick.ac.uk)