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

Author

Michel Lagneau, Dec 09 2013

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A002496, A002522, A134406.

Programs

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 *)