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

5, 13, 13, 17, 31, 61, 239, 0, 127, 41, 0, 73, 131, 0, 61, 1889, 0, 397, 419, 0, 211, 89, 0, 97, 101, 0, 163, 113, 0, 181, 2543, 0, 463, 2789, 211, 5689, 149, 0, 547, 881, 0, 1093, 173, 0, 271, 9293, 0, 673, 491, 0, 1123, 14249, 0, 10909, 3191, 0, 229, 1973, 0, 241

Offset: 1

Author

Amarnath Murthy, Jul 16 2003

Keywords

• nonn

Comments

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).

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

Examples

			a(5) = 31 as (2*5)*31 + 1= 311 as well as (31-1)/10 = 3 are primes.
		

Programs

Mathematica

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}]

Extensions

Corrected by Labos Elemer, Jul 17 2003

Edited and extended by Robert G. Wilson v, Jul 18 2003