This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141293 #22 Aug 10 2025 04:22:01 %S A141293 13,29,41,53,61,73,89,97,109,113,137,149,157,173,181,193,229,233,241, %T A141293 269,277,281,293,313,317,337,349,353,373,389,397,409,421,433,449,457, %U A141293 461,509,521,541,557,569,593,601,613,617,641,653,661,673,701,709,733,757,761,769 %N A141293 Primes p of the form 4*k+1 which are not of the form r^2 + 1. %C A141293 Equivalently, prime factors of numbers of the form x^2 + 1 which themselves are not of this form. %C A141293 Same as A002144 with A002496 removed. %D A141293 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 A141293 a(n) ~ 2n log n. - _Charles R Greathouse IV_, Jun 10 2017 %t A141293 Complement[Select[4*Range[400]+1, PrimeQ], Select[Range[40]^2+1, PrimeQ]] (* _T. D. Noe_, Jun 27 2008 *) %t A141293 Select[Prime[Range[200]],IntegerQ[(#-1)/4]&&!IntegerQ[Sqrt[#-1]]&] (* _Harvey P. Dale_, Jan 04 2015 *) %o A141293 (PARI) forprime(p=3,1000,if(p%4==1&&!issquare((p-1)/4),print1(p,", "))) \\ _Joerg Arndt_, Jul 01 2012 %o A141293 (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 A141293 Cf. A002144, A002145, A002496. %K A141293 nonn %O A141293 1,1 %A A141293 _A.K. Devaraj_, Jun 23 2008 %E A141293 Corrected and extended by _T. D. Noe_ and _N. J. A. Sloane_, Jun 27 2008