%I #42 Aug 07 2023 05:21:41
%S 3,3,3,3,7,3,3,5,7,5,3,5,9,5,9,17,7,3,51,17,7,33,13,39,57,11,21,27,7,
%T 213,15,5,31,3,25,17,21,3,25,107,15,33,3,35,7,23,31,5,19,11,21,65,147,
%U 5,3,33,51,77,45,17,69,53,9,3,67,63,43,63,51,27,73,5
%N Smallest odd k > 1 such that k*2^n - 1 is a prime number.
%C Limit_{N->oo} (Sum_{n=1..N} a(n))/(Sum_{n=1..N} n) = log(2). [[Is there a proof or is this a conjecture? - _Peter Luschny_, Feb 06 2015]]
%C Records: 3, 7, 9, 17, 51, 57, 213, 255, 267, 321, 615, 651, 867, 901, 909, 1001, 1255, 1729, 1905, 2163, 3003, 3007, 3515, 3797, 3825, 4261, 4335, 5425, 5717, 6233, 6525, 6763, 11413, 11919, 12935, 20475, 20869, 25845, 30695, 31039, 31309, 42991, 55999, ... . - _Robert G. Wilson v_, Feb 08 2015
%H Robert G. Wilson v, <a href="/A247202/b247202.txt">Table of n, a(n) for n = 1..10031</a> (first 5000 terms from Pierre CAMI)
%F a(A002235(n)) = 3.
%p f:= proc(n)
%p local k,p;
%p p:= 2^n;
%p for k from 3 by 2 do if isprime(k*p-1) then return k fi od;
%p end proc:
%p seq(f(n), n=1 .. 100); # _Robert Israel_, Feb 05 2015
%t f[n_] := Block[{k = 3, p = 2^n}, While[ !PrimeQ[k*p - 1], k += 2]; k]; Array[f, 70]
%o (PFGW & SCRIPT)
%o SCRIPT
%o DIM k
%o DIM n,0
%o DIMS t
%o OPENFILEOUT myf,a(n).txt
%o LABEL loop1
%o SET n,n+1
%o SET k,1
%o LABEL loop2
%o SET k,k+2
%o SETS t,%d,%d\,;n;k
%o PRP k*2^n-1,t
%o IF ISPRP THEN GOTO a
%o GOTO loop2
%o LABEL a
%o WRITE myf,t
%o GOTO loop1
%o (PARI) a(n) = {k=3; while (!isprime(k*2^n-1), k+=2); k;} \\ _Michel Marcus_, Nov 25 2014
%Y Cf. A126715, A247479.
%K nonn
%O 1,1
%A _Pierre CAMI_, Nov 25 2014