cp's OEIS Frontend

A085956 Smallest prime p such that (2n)*p +1 and (p-1)/(2n) are prime, or 0 if no such prime exists.

%I A085956 #8 Mar 20 2015 22:55:50
%S A085956 5,13,13,17,31,61,239,0,127,41,0,73,131,0,61,1889,0,397,419,0,211,89,
%T A085956 0,97,101,0,163,113,0,181,2543,0,463,2789,211,5689,149,0,547,881,0,
%U A085956 1093,173,0,271,9293,0,673,491,0,1123,14249,0,10909,3191,0,229,1973,0,241
%N A085956 Smallest prime p such that (2n)*p +1 and (p-1)/(2n) are prime, or 0 if no such prime exists.
%C A085956 Primes of the form 16*p + 1 == {1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91} (mod 96).
%C A085956 With rare exceptions, a(3n-1)=0. a(2)=13, a(5)=31 and a(35)=211, all of which are of the form 6n+1. This is true for those 6317 n's which have a solutions less than 10^6. I have no proof! - _Robert G. Wilson v_
%e A085956 a(5) = 31 as (2*5)*31 + 1= 311 as well as (31-1)/10 = 3 are primes.
%t A085956 f[n_] := Block[{k = 1}, While[k < 10^12 && ( !PrimeQ[k] || !PrimeQ[2*n*k + 1] || !PrimeQ[(k - 1)/(2n)] ), k += 2n]; If[k >= 10^12, 0, k]]; Table[ f[n], {n, 1, 61}]
%K A085956 nonn
%O A085956 1,1
%A A085956 _Amarnath Murthy_, Jul 16 2003
%E A085956 Corrected by _Labos Elemer_, Jul 17 2003
%E A085956 Edited and extended by _Robert G. Wilson v_, Jul 18 2003