A249061 a(n) is the least number of successive numbers 1, 2, 3, ... which when added to n produce a prime number.

2, 1, 1, 4, 1, 3, 1, 3, 2, 4, 1, 3, 1, 3, 2, 7, 1, 3, 1, 4, 2, 4, 1, 3, 10, 3, 2, 4, 1, 12, 1, 3, 5, 4, 2, 3, 1, 3, 2, 7, 1, 3, 1, 4, 2, 7, 1, 3, 10, 4, 2, 4, 1, 3, 10, 3, 2, 4, 1, 12, 1, 3, 6, 4, 2, 3, 1, 3, 2, 4, 1, 8, 1, 3, 5, 7, 2, 3, 1, 4, 2, 7, 1, 3

Offset

0,1

Comments

In other words, a(n) = smallest k >= 1 such that n + k(k+1)/2 is a prime. - N. J. A. Sloane, Oct 20 2014

Do we know that a(n) always exists? - N. J. A. Sloane, Oct 20 2014

Conjecturally (Hardy & Littlewood conjecture F), a(n) exists for all n. - Charles R Greathouse IV, Oct 21 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Example

a(1)=1 because 1+[1]=2 which is prime.
a(2)=1 because 2+[1] =3 which is prime.
a(3)=4 because 3+[1+2+3+4]=13 which is prime, and intermediate sums are composite.

Mathematica

lst = {}; Do[k = 1; While[! PrimeQ[n + k (k + 1)/2], k++]; AppendTo[lst, k], {n, 0, 100}]; lst (* Ivan N. Ianakiev, Oct 21 2014 *)

Prog

(PARI) a(n) = {k=1; while (!isprime(n + k*(k+1)/2), k++); k; } \\ Michel Marcus, Oct 21 2014

Crossrefs

Sequence in context: A131350 A131087 A105475 * A334178 A210209 A328649

Adjacent sequences: A249058 A249059 A249060 * A249062 A249063 A249064

Keyword

nonn,easy

Author

Gil Broussard, Oct 20 2014

Extensions

Definition edited by N. J. A. Sloane, Oct 20 2014

Mathematica code adapted to the offset by Vincenzo Librandi Oct 21 2014

Status

approved