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%I #19 Mar 28 2015 04:23:34
%S 2,11,17,23,25,31,39,41,45,51,53,56,57,59,65,67,73,76,79,81,83,85,87,
%T 91,95,97,99,100,101,105,109,111,113,115,123,125,129,133,137,141,143,
%U 147,149,151,153,154,157,159,163,165,167,170,171,175,179,181,185,187,189,193,195,197,199,201,203,207,209,213,215,219,221,225
%N Numbers n such that the difference between n^2 and largest prime less than n^2 is not prime.
%C Indices of terms in A056927 that are not prime.
%H Richard L. Francis, <a href="http://www.math-cs.ucmo.edu/~mjms/2004.1/Francis-Squares.pdf">Between consecutive squares</a>, Missouri Journal of Mathematical Sciences, Volume 16 Issue #1 - Winter 2004.
%e a(1) = 2, since 2^2 - 3 = 1.
%e a(2) = 11, since 11^2 - 113 = 8.
%e a(3) = 17, since 17^2 - 283 = 6.
%e a(4) = 23, since 23^2 - 523 = 6.
%t f[n_] := n^2 - NextPrime[n^2, -1]; Select[Range[2, 230], !PrimeQ[f[#]] &]
%o (PARI) lista(nn) = for (n=2, nn, if (!isprime(n^2-precprime(n^2)), print1(n, ", "))); \\ _Michel Marcus_, Mar 22 2015
%Y Cf. A000040, A000290, A056927, A053001.
%K nonn,easy
%O 1,1
%A _Carlos Eduardo Olivieri_, Mar 17 2015
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