A353697 a(n) is the least prime p such that, if q is the next prime after p and d = q-p, then p-n*d, p+n*d, q-n*d and q+n*d are all prime.

47, 131641, 11, 2417, 53, 17, 8389, 53, 43, 167, 167, 1171, 137537, 167, 41, 557, 80111, 241, 5387, 131, 59, 6917, 13187, 59, 157, 2861, 887, 14251, 367, 229, 1367, 72767, 71, 257, 233, 163, 4297, 233, 149, 263, 257, 547, 4831, 1499, 101, 1217, 66191, 101, 647, 353, 919, 7759, 18553, 223, 971

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 11 because p = 11 is prime, the next prime is q = 13, d = 2, and p-3*d = 5, p+3*d = 17, q-3*d = 7, and q+3*d = 19 are prime; and this is the least prime that works.

Maple

f:= proc(n) local p, q, c;
  q:= 2:
  do
   p:= q; q:= nextprime(q); d:= q-p;
   if isprime(p-n*d) and isprime(p+n*d) and isprime(q-n*d) and isprime(q+n*d) then return p fi
  od;
end proc:
map(f, [$1..100]);

Mathematica

a[n_] := Module[{p = 2, q = 3, d = 1}, While[! AllTrue[{p - n*d, p + n*d, q - n*d, q + n*d}, # > 0 && PrimeQ[#] &], p = q; q = NextPrime[q]; d = q - p]; p]; Array[a, 55] (* Amiram Eldar, Sep 06 2022 *)

Prog

(Python)
from sympy import isprime, nextprime
def a(n):
    p = nextprime(2*n); q = nextprime(p); d = q-p
    while not all(isprime(t) for t in [p-n*d, p+n*d, q-n*d, q+n*d]):
        p = q; q = nextprime(q); d = q-p
    return p
print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Sep 05 2022

Crossrefs

Sequence in context: A093940 A237512 A224468 * A328364 A087533 A292071

Adjacent sequences: A353694 A353695 A353696 * A353698 A353699 A353700

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, Sep 05 2022

Status

approved