A141881 Primes congruent to 1 mod 20.

41, 61, 101, 181, 241, 281, 401, 421, 461, 521, 541, 601, 641, 661, 701, 761, 821, 881, 941, 1021, 1061, 1181, 1201, 1301, 1321, 1361, 1381, 1481, 1601, 1621, 1721, 1741, 1801, 1861, 1901, 2081, 2141, 2161, 2221, 2281, 2341, 2381, 2441, 2521, 2621, 2741, 2801

Offset: 1

Author

N. J. A. Sloane, Jul 11 2008

Keywords

• nonn
• easy

Comments

Such a prime is representable by either both or neither of the quadratic forms x^2 + 20 y^2 and x^2 + 100 y^2. See the Brink link. - Robert Israel, Jun 11 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893

Crossrefs

Cf. A000040, A105854, A141882, A141883.

Programs

Magma

[p: p in PrimesUpTo(3000) | p mod 20 eq 1 ]; // Vincenzo Librandi, Aug 15 2012

Maple

select(isprime,[seq(20*i+1,i=1..1000)]); # Robert Israel, Jun 11 2014

Mathematica

Select[Range[1,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)
Select[Prime[Range[500]],Mod[#,20]==1&] (* Harvey P. Dale, Nov 23 2024 *)

PARI

is(n)=isprime(n) && n%20==1 \\ Charles R Greathouse IV, Jul 01 2016