A338030 Primes p such that reverse(p), reverse(2*p) and reverse(2*reverse(p)) are all primes, where reverse = A004086.

7, 17, 37, 71, 73, 167, 181, 191, 353, 373, 389, 761, 787, 797, 929, 983, 1753, 1879, 3571, 7057, 7177, 7507, 7717, 7879, 9349, 9439, 9781, 9787, 15053, 15227, 15307, 15451, 15551, 15667, 15679, 15791, 15919, 16061, 16073, 16453, 16547, 16561, 16747, 16883, 16979, 17471, 17909, 17971, 18427

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 09 2020

Keywords

• nonn
• base

Examples

			a(3) = 37 is a term because 37, reverse(37)=73, reverse(2*37)=47 and reverse(2*73)=641 are prime.
		

Links

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

Crossrefs

Cf. A004086, A007500.

Programs

Maple

rev:= proc(n) local L,k;
  L:= convert(n,base,10);
  add(L[-k]*10^(k-1),k=1..nops(L))
end proc:
filter:= proc(n) local r;
if not isprime(n) then return false fi;
  r:= rev(n);
isprime(r) and isprime(rev(2*n)) and isprime(rev(2*r))
end proc:
select(filter, [seq(i,i=3..20000,2)]);

Mathematica

With[{rev = IntegerReverse}, Select[Range[20000], AllTrue[{#, rev[#], rev[2*#], rev[2*rev[#]]}, PrimeQ] &]] (* Amiram Eldar, Oct 10 2020 *)

PARI

rev(n) = fromdigits(Vecrev(digits(n))); \\ A004086
isok(p) = if (isprime(p), my(r=rev(p)); isprime(r) && isprime(rev(2*p)) && isprime(rev(2*r))); \\ Michel Marcus, Oct 10 2020