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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A260310 A122237 A307162 * A280581 A278755 A016625

Adjacent sequences:  A233415 A233416 A233417 * A233419 A233420 A233421

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 09 2013

STATUS

approved

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Last modified October 23 12:04 EDT 2019. Contains 328345 sequences. (Running on oeis4.)