A376522 Numbers k such that (prime(j)-1)^2 + 1 is prime for k <= j <= k + 2.

1, 2, 3, 53, 678, 1990, 5154, 5632, 6412, 8022, 8715, 11211, 13182, 16632, 16793, 17263, 18755, 19484, 23458, 25693, 26960, 28005, 28492, 29024, 31055, 36084, 41707, 44434, 44642, 44936, 46602, 48630, 48631, 54274, 56131, 58219, 58879, 69935, 74008, 76310, 77836, 83540, 83686, 88526, 88877, 91217

Offset

1,2

Comments

The first three k such that (prime(j)-1)^2 + 1 is prime for k <= j <= k + 3 are 1, 2, and 48630.

The first two k such that (prime(j)-1)^2 + 1 is prime for k <= j <= k + 4 are 1 and 546158.

The first k such that (prime(j)-1)^2 + 1 is prime for k <= j <= k + 5 is 2296966.

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Example

a(4) = 53 is a term because the 53rd, 54th and 55th primes are 241, 251, 257, and (241-1)^2 + 1 = 57601, (251-1)^2 + 1 = 62501, and (257-1)^2 + 1 = 65537 are all prime.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
J:= select(i -> isprime((P[i]-1)^2+1), [$1..nops(P)]):
J[select(i -> J[i+2]=J[i]+2, [$1..nops(J)-2])];

Crossrefs

Cf. A000040, A127435, A173446, A376605.

Sequence in context: A342408 A062641 A339920 * A344732 A037424 A155088

Adjacent sequences: A376519 A376520 A376521 * A376523 A376524 A376525

Keyword

nonn

Author

Robert Israel, Sep 29 2024

Status

approved