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

1,1

Comments

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

Links

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

Example

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

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}]

Crossrefs

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

Sequence in context: A321217 A095748 A350699 * A268923 A172287 A062579

Adjacent sequences: A235917 A235918 A235919 * A235921 A235922 A235923

Keyword

nonn

Author

Zhi-Wei Sun, Jan 17 2014

Status

approved