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

1,1

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

Links

Table of n, a(n) for n=1..60.

Example

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

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}]

Crossrefs

Sequence in context: A274302 A274300 A051899 * A232610 A235337 A151994

Adjacent sequences: A085953 A085954 A085955 * A085957 A085958 A085959

Keyword

nonn

Author

Amarnath Murthy, Jul 16 2003

Extensions

Corrected by Labos Elemer, Jul 17 2003

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

Status

approved