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A176983 Primes p such that smallest prime q > p^2 is of form q = p^2 + k^2. 5

%I

%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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Last modified April 22 15:23 EDT 2021. Contains 343177 sequences. (Running on oeis4.)