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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.

%I A233418 #9 Dec 10 2013 14:55:54
%S A233418 1,3,8,7,32,31,30,29,28,27,44,43,42,41,96,95,188,187,186,185,364,363,
%T A233418 362,361,360,359,358,357,356,355,354,353,352,351,502,501,500,499,498,
%U A233418 497,3396,3395,3394,3393,3392,3391,3578,3577,3576,3575,3574,3573,3572
%N 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.
%H A233418 Michel Lagneau, <a href="/A233418/b233418.txt">Table of n, a(n) for n = 0..325</a>
%e A233418 a(0) = 1 because  1^2+1 is prime.
%e A233418 a(1) = 3 because  3^2+1 is composite, but 4^2+1 is prime.
%e A233418 a(2) = 8 because  8^2+1, 9^2+1 are composites, but 10^2+1 is prime.
%e A233418 a(3) = 7 because  7^2+1, 8^2+1 and 9^2+1 are composites, but 10^2+1 is prime.
%p A233418 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:
%t A233418 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 *)
%Y A233418 Cf. A002496, A002522, A134406.
%K A233418 nonn
%O A233418 0,2
%A A233418 _Michel Lagneau_, Dec 09 2013