A085759 Prime powers of the form 4n+1.

1, 5, 9, 13, 17, 25, 29, 37, 41, 49, 53, 61, 73, 81, 89, 97, 101, 109, 113, 121, 125, 137, 149, 157, 169, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 289, 293, 313, 317, 337, 349, 353, 361, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521

Offset: 1

Author

Lekraj Beedassy, Jul 22 2003

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning, Restrained domination in self-complementary graphs, Preprint, Discussiones Mathematicae Graph Theory (2019), 1-13.
• Eric Weisstein's World of Mathematics, Paley Graph

Crossrefs

Subsequence of A000961. A002144 is a subsequence.

Programs

Magma

[1] cat [4*k+1:k in [1..140]|IsPrimePower(4*k+1)]; // Marius A. Burtea, Sep 07 2019

Mathematica

{1}~Join~Select[1 + 4 Range[130], PrimePowerQ] (* Michael De Vlieger, Aug 29 2019 *)

PARI

list(lim)=my(v=List([1])); forprime(p=5,lim\=1, if(p%4==1, listput(v,p))); for(e=2,logint(lim,3), forprime(p=3,sqrtnint(lim,e), if(e%2==0 || p%4==1, listput(v,p^e)))); Set(v) \\ Charles R Greathouse IV, Jul 12 2018

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Jul 12 2018

Extensions

Corrected and extended by Ray Chandler, Aug 10 2003