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%I #18 Jun 10 2017 23:24:31
%S 13,29,41,53,61,73,89,97,109,113,137,149,157,173,181,193,229,233,241,
%T 269,277,281,293,313,317,337,349,353,373,389,397,409,421,433,449,457,
%U 461,509,521,541,557,569,593,601,613,617,641,653,661,673,701,709,733,757,761,769
%N Primes p of the form 4*k+1 which are not of the form r^2 + 1.
%C Equivalently, prime factors of numbers of the form x^2 + 1 which themselves are not of this form.
%C Same as A002144 with A002496 removed.
%D A. K. Devaraj, "Euler's Generalization of Fermat's Theorem-A Further Generalization", in ISSN #1550-3747, Proceedings of Hawaii Intl Conference on Statistics, Mathematics & Related Fields, 2004.
%F a(n) ~ 2n log n. - _Charles R Greathouse IV_, Jun 10 2017
%t Complement[Select[4*Range[400]+1, PrimeQ], Select[Range[40]^2+1, PrimeQ]] - _T. D. Noe_, Jun 27 2008
%t Select[Prime[Range[200]],IntegerQ[(#-1)/4]&&!IntegerQ[Sqrt[#-1]]&] (* _Harvey P. Dale_, Jan 04 2015 *)
%o (PARI) forprime(p=3,1000,if(p%4==1&&!issquare((p-1)/4),print1(p,", "))) \\ _Joerg Arndt_, Jul 01 2012
%o (PARI) list(lim)=my(v=List()); forprime(p=2,lim, if(p%4==1, listput(v,p))); v=setminus(Set(v), vector(sqrtint(lim\4),i,4*i^2+1)) \\ _Charles R Greathouse IV_, Jun 10 2017
%Y Cf. A002144, A002145, A002496.
%K nonn
%O 1,1
%A _A.K. Devaraj_, Jun 23 2008
%E Corrected and extended by T. D. Noe and _N. J. A. Sloane_, Jun 27 2008
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