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A263046 Smallest number k>2 such that k*2^n + 1 is a prime number.

%I A263046 #24 Oct 31 2015 15:15:04
%S A263046 4,3,3,5,6,3,3,5,3,15,12,6,3,5,4,5,12,6,3,11,7,11,25,20,10,5,7,15,12,
%T A263046 6,3,35,18,9,12,6,3,15,10,5,6,3,9,9,15,35,19,27,15,14,7,14,7,20,10,5,
%U A263046 27,29,54,27,31,36,18,9,12,6,3,9,31,23,39,39,40,20,10,5,58
%N A263046 Smallest number k>2 such that k*2^n + 1 is a prime number.
%C A263046 If k = 2^j then 2^(n+j) + 1 is a Fermat prime.
%C A263046 a(n) = 3 if and only if 3*2^n + 1 is a prime; that is, n belongs to A002253. - _Altug Alkan_, Oct 08 2015
%C A263046 a(n+1) >= ceiling(a(n)/2). If a(n) is even then a(n+1) = a(n)/2. - _Robert Israel_, Oct 08 2015
%H A263046 Pierre CAMI, <a href="/A263046/b263046.txt">Table of n, a(n) for n = 0..10000</a>
%e A263046 3*2^1 + 1 = 7 (prime), so a(1)=3:
%e A263046 3*2^2 + 1 = 13 (prime), so a(2)=3;
%e A263046 3*2^3 + 1 = 25 (composite), 4*2^3 + 1 = 33 (composite), 5*2^3 - 1 = 41 (prime), so a(3)=5.
%p A263046 f:= proc(n) local k;
%p A263046     for k from 3 do if isprime(k*2^n+1) then return k fi od
%p A263046   end proc:
%p A263046 seq(f(n),n=1..100); # _Robert Israel_, Oct 08 2015
%t A263046 Table[k = 3; While[! PrimeQ[k 2^n + 1], k++]; k, {n, 76}] (* _Michael De Vlieger_, Oct 08 2015 *)
%o A263046 (PARI) a(n) = {k=3; while (! isprime(k*2^n+1), k++); k;} \\ _Michel Marcus_, Oct 08 2015
%Y A263046 Cf. A247479, A262994.
%K A263046 nonn
%O A263046 0,1
%A A263046 _Pierre CAMI_, Oct 08 2015