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Least k such that (2n + k) + 1 and (2n*k) + 1 are both primes.
2

%I #6 Jul 25 2015 01:16:12

%S 2,18,6,2,6,6,2,6,4,2,18,4,2,12,6,8,12,16,20,6,10,2,6,4,2,6,24,2,30,

%T 10,26,18,6,2,36,6,8,6,4,8,66,4,2,24,6,14,12,6,2,6,4,32,30,4,26,18,34,

%U 50,30,10,8,12,52,2,18,16,2,60,10,32,6,4,2,30,12,14,24,6,14,30,10,14,6,4,8

%N Least k such that (2n + k) + 1 and (2n*k) + 1 are both primes.

%C For n>1 a(n) is even and also if a(n) = m then a(m/2) = 2n.

%e a(4) = 2, 8 + 2 + 1 = 11 and 8*2 + 1 = 17 are both prime.

%t f[n_] := Block[{k = 1}, While[ !PrimeQ[2n + k + 1] || ! PrimeQ[2n*k + 1], k++ ]; k]; Table[ f[n], {n, 85}] (* _Robert G. Wilson v_, Apr 24 2004 *)

%Y Twice A093312.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Apr 14 2004

%E Edited, corrected and extended by _Robert G. Wilson v_, Apr 24 2004