A396687 Smallest k > 0 such that 2*prime(n) - prime(n-k) is prime.

1, 2, 2, 2, 2, 4, 2, 3, 3, 1, 3, 6, 2, 1, 2, 4, 1, 3, 2, 4, 6, 4, 6, 2, 2, 2, 7, 6, 4, 2, 5, 3, 3, 2, 1, 7, 6, 1, 2, 4, 8, 6, 6, 9, 1, 10, 4, 8, 2, 3, 6, 2, 1, 1, 2, 8, 1, 3, 11, 5, 2, 7, 6, 6, 2, 5, 5, 3, 2, 6, 5, 1, 5, 7, 5, 4, 3, 2, 4, 2, 2, 4, 3, 5, 4, 14

Offset

3,2

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 3..10000

Formula

A078611(n) = prime(n) - prime(n - a(n)).

Example

a(3) = 1, because prime(3) = 5 and prime(3 - a(3)) = prime(2) = 3 and 5 + (5 - 3) = 7 is prime.
a(14) = 6, because 6 is the smallest k > 0 for which 2 * prime(14) - prime(14 - k) is prime.

Mathematica

a[n_]:=Module[{k=1}, While[!PrimeQ[2Prime[n]-Prime[n-k]], k++]; k]; Array[a, 86, 3] (* Stefano Spezia, Jun 02 2026 *)

Prog

(PARI) a(n)= if(n<3, 0, my(p=prime(n), k=0); until(isprime(p*2-prime(n-k++)), ); k)
(PARI) a(n) = {my(p = prime(n), ptwice = 2*p, other); forprime(q = p+1, ptwice-1, if(isprime(ptwice - q), other = ptwice - q; break)); n-primepi(other)} \\ David A. Corneth, Jun 02 2026

Crossrefs

Cf. A000040, A078611, A179835.

Sequence in context: A366763 A138011 A036555 * A046927 A366563 A351411

Adjacent sequences: A396684 A396685 A396686 * A396689 A396691 A396694

Keyword

easy,nonn

Author

Ruud H.G. van Tol, Jun 02 2026

Status

approved