A357426 Primes p such that p^2+4 is a prime times 5^k for some k >= 1.

11, 19, 31, 41, 61, 71, 79, 89, 109, 131, 139, 149, 151, 181, 191, 239, 241, 251, 379, 389, 409, 421, 461, 499, 509, 541, 599, 631, 659, 661, 709, 719, 769, 811, 919, 1009, 1019, 1021, 1031, 1109, 1129, 1151, 1201, 1231, 1291, 1361, 1399, 1409, 1451, 1489, 1549, 1601, 1621, 1721, 1789, 1871, 1889, 1931, 2011, 2039, 2069, 2131, 2179, 2221, 2251, 2309, 2341, 2351

Offset: 1

Author

J. M. Bergot and Robert Israel, Sep 27 2022

Keywords

• nonn

Comments

All terms == 1 or 9 (mod 10).

Examples

			a(4) = 41 is a term because 41 is prime and 41^2+4 = 1685 = 337 * 5^1 where 337 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Disjoint from A062324.

Programs

Maple

filter:= proc(p) local v;
  if not isprime(p) then return false fi;
  v:= p^2+4;
  isprime(v/5^padic:-ordp(v,5))
end proc:
filter(11):= true:
select(filter, [seq(seq(10*i+j, j= [1,9]),i=1..1000)]);

Mathematica

q[p_] := (e = IntegerExponent[m = p^2 + 4, 5]) > 0 && (m==5^e || PrimeQ[m/5^e]); Select[Prime[Range[350]], q] (* Amiram Eldar, Sep 28 2022 *)