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 A141293 Primes p of the form 4*k+1 which are not of the form r^2 + 1. 2
 13, 29, 41, 53, 61, 73, 89, 97, 109, 113, 137, 149, 157, 173, 181, 193, 229, 233, 241, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 593, 601, 613, 617, 641, 653, 661, 673, 701, 709, 733, 757, 761, 769 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, prime factors of numbers of the form x^2 + 1 which themselves are not of this form. Same as A002144 with A002496 removed. REFERENCES 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. LINKS FORMULA a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 10 2017 MATHEMATICA Complement[Select[4*Range[400]+1, PrimeQ], Select[Range[40]^2+1, PrimeQ]] - T. D. Noe, Jun 27 2008 Select[Prime[Range[200]], IntegerQ[(#-1)/4]&&!IntegerQ[Sqrt[#-1]]&] (* Harvey P. Dale, Jan 04 2015 *) PROG (PARI) forprime(p=3, 1000, if(p%4==1&&!issquare((p-1)/4), print1(p, ", "))) \\ Joerg Arndt, Jul 01 2012 (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 CROSSREFS Cf. A002144, A002145, A002496. Sequence in context: A036974 A045472 A240950 * A120827 A320631 A309356 Adjacent sequences:  A141290 A141291 A141292 * A141294 A141295 A141296 KEYWORD nonn AUTHOR A.K. Devaraj, Jun 23 2008 EXTENSIONS Corrected and extended by T. D. Noe and N. J. A. Sloane, Jun 27 2008 STATUS approved

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Last modified October 18 22:17 EDT 2019. Contains 328211 sequences. (Running on oeis4.)