A256454 a(n) = smallest prime(j) > a(n-1) such that prime(j+1) - prime(j) = 2n, a(0) = 2.

2, 3, 7, 23, 89, 139, 199, 293, 1831, 1913, 3089, 3229, 4177, 5531, 5953, 6491, 10799, 11743, 12853, 30593, 33247, 34981, 36389, 81463, 86629, 95651, 103237, 106033, 153191, 181303, 189067, 190409, 288583, 294563, 326369, 399283, 507217, 514967, 570253, 642281, 815729, 841459, 979567

Offset

0,1

Links

Bill McEachen and Robert G. Wilson v, Table of n, a(n) for n = 0..180

Formula

a(n) = A253899(n) - 2n for n > 0.

Example

a(4) = 89 since 89=97-8, and this is the first time this gap is seen after smaller gaps of 1,2,4,6 are satisfied.

Mathematica

lst = {2}; p = 2; q = 3; gp = 2; While[ gp != 86, While[q - p != gp, p = q; q = NextPrime@ p]; AppendTo[lst, p]; Print@ p; gp += 2]; lst

Prog

(Python) from sympy import sieve
A256454 = [2]
for j in range(2, 90000):
    if sieve[j+1] - sieve[j] == 2 * len(A256454): A256454.append(sieve[j])
print(A256454) # Karl-Heinz Hofmann, May 03 2022

Crossrefs

Cf. A000230, A000101, A253899 (upper end).

Sequence in context: A335366 A002386 A000230 * A133429 A087770 A237359

Adjacent sequences: A256451 A256452 A256453 * A256455 A256456 A256457

Keyword

nonn

Author

Bill McEachen and Robert G. Wilson v, Mar 29 2015

Status

approved