A233418 a(n) is the smallest number k > 0 such that k^2+1, (k+1)^2+1,...,(k+n)^2+1 are composite numbers.

1, 3, 8, 7, 32, 31, 30, 29, 28, 27, 44, 43, 42, 41, 96, 95, 188, 187, 186, 185, 364, 363, 362, 361, 360, 359, 358, 357, 356, 355, 354, 353, 352, 351, 502, 501, 500, 499, 498, 497, 3396, 3395, 3394, 3393, 3392, 3391, 3578, 3577, 3576, 3575, 3574, 3573, 3572

Offset

0,2

Links

Michel Lagneau, Table of n, a(n) for n = 0..325

Example

a(0) = 1 because  1^2+1 is prime.
a(1) = 3 because  3^2+1 is composite, but 4^2+1 is prime.
a(2) = 8 because  8^2+1, 9^2+1 are composites, but 10^2+1 is prime.
a(3) = 7 because  7^2+1, 8^2+1 and 9^2+1 are composites, but 10^2+1 is prime.

Maple

for n from 0 to 60 do: ii:=0:for k from 1 to 10^8 while(ii=0) do:i:=0:for m from 0 to n while(type((k+m)^2+1, prime)=false ) do :i:=i+1:od:if i=n then ii:=1: printf(`%d, `, k):else fi:od:od:

Mathematica

nn = 50; t = Table[0, {nn}]; cnt = 0; k = 0; While[cnt < nn, k++; i = 0; While[! PrimeQ[(k + i)^2 + 1], i++]; If[i < nn && t[[i + 1]] == 0, t[[i + 1]] = k; cnt++]]; t (* T. D. Noe, Dec 10 2013 *)

Crossrefs

Cf. A002496, A002522, A134406.

Sequence in context: A342662 A122237 A307162 * A280581 A278755 A016625

Adjacent sequences: A233415 A233416 A233417 * A233419 A233420 A233421

Keyword

nonn

Author

Michel Lagneau, Dec 09 2013

Status

approved