A345346 Primes whose digit reversal is twice a prime.

41, 43, 47, 83, 229, 241, 263, 283, 419, 431, 433, 439, 479, 491, 601, 607, 641, 643, 647, 661, 683, 811, 853, 857, 859, 877, 2039, 2063, 2069, 2083, 2099, 2203, 2207, 2251, 2273, 2281, 2287, 2411, 2417, 2423, 2437, 2467, 2473, 2617, 2621, 2663, 2671, 2677, 2683, 2687, 2689, 2801, 2819, 2837

Offset: 1

Author

J. M. Bergot and Robert Israel, Jun 14 2021

Keywords

• nonn
• base

Examples

			a(3) = 47 is a term because 47 and 74/2 = 37 are primes.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A085778 and A273892.

Programs

Maple

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(n) isprime(n) and numtheory:-bigomega(revdigs(n))=2 end proc:
select(filter, [seq(seq(seq(i*10^d+j,j=1..10^d-1,2),i=2..8,2),d=1..4)]);

PARI

isok(p) = if (isprime(p), my(r=fromdigits(Vecrev(digits(p)))); if (!(r%2), isprime(r/2))); \\ Michel Marcus, Jun 15 2021

Python

from sympy import isprime, primerange
def ok(p): t = int(str(p)[::-1]); return t%2 == 0 and isprime(t//2)
print(list(filter(ok, primerange(1, 2838)))) # Michael S. Branicky, Jun 16 2021