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%I #6 Nov 04 2013 10:04:25
%S 2,5,7,13,17,37,47,67,73,97,103,137,163,167,193,233,277,281,293,307,
%T 313,317,347,373,389,421,439,461,463,487,499,503,547,571,577,593,607,
%U 613,661,677,691,701,739,743,769,787,821,823,827,829,853,883,953,967,983
%N Primes p such that smallest prime q > p^2 is of form q = p^2 + k^2.
%C By Fermat's 4n+1 theorem, q must be congruent to 1 (mod 4).
%C Corresponding values of k: 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6, 2, 2, 4, 2. - _Zak Seidov_, Nov 04 2013
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Fermats4nPlus1Theorem.html">Fermat's 4n+1 Theorem</a>
%e 17 is here because 293 is the first prime after 17^2 and 293 = 17^2 + 2^2.
%t Select[Prime[Range[200]], IntegerQ[Sqrt[NextPrime[ #^2] - #^2]] & ]
%Y Cf. A000040, A000290, A002144, A159828.
%Y A062324 is subsequence. - _Zak Seidov_, Nov 04 2013
%K nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2010
%E Edited and extended by _T. D. Noe_, May 12 2010
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