A141293 Primes p of the form 4*k+1 which are not of the form r^2 + 1.

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

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

Table of n, a(n) for n=1..56.

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 * A339956 A352926 A339989

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