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%I #43 Feb 01 2024 06:09:20
%S 2,3,7,17,41,239,577,665857,9369319,63018038201,489133282872437279,
%T 19175002942688032928599,
%U 123426017006182806728593424683999798008235734137469123231828679
%N Primes whose squares are not the sums of two consecutive nonsquares.
%C Primes of the form A257282(k).
%C 2 is in this sequence, and an odd prime p is in the sequence iff either (p^2 - 1)/2 or (p^2 + 1)/2 is a square. - _Wolfdieter Lang_, May 07 2015
%C According to the Neretin comment in A257282, and as the primes of A001333 are in A086395, this is (apart from the 2) the same as A086395. - _R. J. Mathar_, Jan 31 2024
%e 2 is in the sequence because it is prime and its square 4 is in A256944: 4 is not a sum of consecutive numbers.
%e 3 is in the sequence because it is prime and its square 9 is in A256944: 9 = 2^2 + 5.
%e 7 is in the sequence because it is prime and its square 49 is in A256944: 49 = 24 + 5^2.
%e 5 is not in the sequence because neither 12 nor 13 is a square.
%t lim = 1000000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Sqrt[#] & /@ Select[Range@ Floor[Sqrt[lim]]^2, ! MemberQ[s, #] &] , PrimeQ] (* _Michael De Vlieger_, Apr 29 2015 *)
%Y Cf. A000290, A001601, A088165, A256944.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Apr 29 2015
%E Name clarified by _Michael De Vlieger_ and _Jon E. Schoenfield_, May 03 2015
%E Edited by _Wolfdieter Lang_, May 07 2015
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