A235920 Primes p with prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) both prime.

17, 31, 41, 43, 61, 71, 83, 103, 109, 173, 181, 211, 271, 349, 353, 541, 661, 673, 743, 811, 911, 953, 971, 1171, 1429, 1471, 1483, 1723, 1787, 2053, 2203, 2579, 2749, 3019, 3299, 3391, 3433, 3463, 3727, 3917, 4003, 4021, 4049, 4243, 4447, 4567, 4657, 4729, 4801, 4993

Offset: 1

Author

Zhi-Wei Sun, Jan 17 2014

Keywords

• nonn

Comments

By the conjecture in A235919, this sequence should have infinitely many terms.

Examples

			a(1) = 17 with prime(17) - 17 + 1 =   59 - 16 = 43 and (17^2 - 1)/4 - prime(17) = 72 - 59 = 13 both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A234695, A235727, A235806, A235914, A235919.

Programs

Mathematica

PQ[n_]:=n>0&&PrimeQ[n]
p[n_]:=PrimeQ[Prime[n]-n+1]&&PQ[(n^2-1)/4-Prime[n]]
n=0;Do[If[p[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]