cp's OEIS Frontend

A104080 Smallest prime >= 2^n.

%I A104080 #58 Sep 01 2024 10:25:24
%S A104080 2,2,5,11,17,37,67,131,257,521,1031,2053,4099,8209,16411,32771,65537,
%T A104080 131101,262147,524309,1048583,2097169,4194319,8388617,16777259,
%U A104080 33554467,67108879,134217757,268435459,536870923,1073741827,2147483659
%N A104080 Smallest prime >= 2^n.
%H A104080 Jinyuan Wang, <a href="/A104080/b104080.txt">Table of n, a(n) for n = 0..1000</a>
%F A104080 a(n) = A014210(n), n <> 1. - _R. J. Mathar_, Oct 14 2008
%F A104080 Sum_{n >= 0} 1/a(n) = A338475 + 1/6 = 1.4070738... (because 1/6 = 1/2 - 1/3). - _Bernard Schott_, Nov 01 2020
%F A104080 From _Gus Wiseman_, Jun 03 2024: (Start)
%F A104080 a(n) = A007918(2^n).
%F A104080 a(n) = 2^n + A092131(n).
%F A104080 a(n) = prime(A372684(n)).
%F A104080 (End)
%t A104080 Join[{2,2},NextPrime[#]&/@(2^Range[2,40])]  (* _Harvey P. Dale_, Jan 26 2011 *)
%t A104080 NextPrime[2^Range[0,50]-1]  (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)
%o A104080 (PARI) g(n,b=2) = for(x=0,n,print1(nextprime(b^x)","))
%o A104080 (PARI) a(n) = nextprime(2^n); \\ _Michel Marcus_, Nov 01 2020
%Y A104080 Cf. A104081, A338475.
%Y A104080 Except initial terms and offset, same as A014210 and A203074.
%Y A104080 The opposite (greatest prime <= 2^n) is A014234, indices A007053.
%Y A104080 The distance from 2^n is A092131, opposite A013603.
%Y A104080 Counting zeros instead of both bits gives A372474, cf. A035103, A211997.
%Y A104080 Counting ones instead of both bits gives A372517, cf. A014499, A061712.
%Y A104080 For squarefree instead of prime we have A372683, cf. A143658, A372540.
%Y A104080 The indices of these prime are given by A372684.
%Y A104080 Cf. A007918, A007920, A029837, A035100, A049095, A130739.
%K A104080 easy,nonn
%O A104080 0,1
%A A104080 _Cino Hilliard_, Mar 03 2005