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

%I A357426 #17 Oct 02 2022 19:14:31
%S A357426 11,19,31,41,61,71,79,89,109,131,139,149,151,181,191,239,241,251,379,
%T A357426 389,409,421,461,499,509,541,599,631,659,661,709,719,769,811,919,1009,
%U A357426 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 A357426 Primes p such that p^2+4 is a prime times 5^k for some k >= 1.
%C A357426 All terms == 1 or 9 (mod 10).
%H A357426 Robert Israel, <a href="/A357426/b357426.txt">Table of n, a(n) for n = 1..10000</a>
%e A357426 a(4) = 41 is a term because 41 is prime and 41^2+4 = 1685 = 337 * 5^1 where 337 is prime.
%p A357426 filter:= proc(p) local v;
%p A357426   if not isprime(p) then return false fi;
%p A357426   v:= p^2+4;
%p A357426   isprime(v/5^padic:-ordp(v,5))
%p A357426 end proc:
%p A357426 filter(11):= true:
%p A357426 select(filter, [seq(seq(10*i+j, j= [1,9]),i=1..1000)]);
%t A357426 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 A357426 Disjoint from A062324.
%K A357426 nonn
%O A357426 1,1
%A A357426 _J. M. Bergot_ and _Robert Israel_, Sep 27 2022