A357426 - OEIS

%I #17 Oct 02 2022 19:14:31

%S 11,19,31,41,61,71,79,89,109,131,139,149,151,181,191,239,241,251,379,

%T 389,409,421,461,499,509,541,599,631,659,661,709,719,769,811,919,1009,

%U 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

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

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

%H Robert Israel, <a href="/A357426/b357426.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(p) local v;

%p   if not isprime(p) then return false fi;

%p   v:= p^2+4;

%p   isprime(v/5^padic:-ordp(v,5))

%p end proc:

%p filter(11):= true:

%p select(filter, [seq(seq(10*i+j, j= [1,9]),i=1..1000)]);

%t 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 *)

%Y Disjoint from A062324.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Sep 27 2022