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Primes p such that reverse(p), reverse(2*p) and reverse(2*reverse(p)) are all primes, where reverse = A004086.
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%I #17 Oct 13 2020 19:23:04

%S 7,17,37,71,73,167,181,191,353,373,389,761,787,797,929,983,1753,1879,

%T 3571,7057,7177,7507,7717,7879,9349,9439,9781,9787,15053,15227,15307,

%U 15451,15551,15667,15679,15791,15919,16061,16073,16453,16547,16561,16747,16883,16979,17471,17909,17971,18427

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

%H Robert Israel, <a href="/A338030/b338030.txt">Table of n, a(n) for n = 1..10000</a>

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

%p rev:= proc(n) local L,k;

%p L:= convert(n,base,10);

%p add(L[-k]*10^(k-1),k=1..nops(L))

%p end proc:

%p filter:= proc(n) local r;

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

%p r:= rev(n);

%p isprime(r) and isprime(rev(2*n)) and isprime(rev(2*r))

%p end proc:

%p select(filter, [seq(i,i=3..20000,2)]);

%t With[{rev = IntegerReverse}, Select[Range[20000], AllTrue[{#, rev[#], rev[2*#], rev[2*rev[#]]}, PrimeQ] &]] (* _Amiram Eldar_, Oct 10 2020 *)

%o (PARI) rev(n) = fromdigits(Vecrev(digits(n))); \\ A004086

%o isok(p) = if (isprime(p), my(r=rev(p)); isprime(r) && isprime(rev(2*p)) && isprime(rev(2*r))); \\ _Michel Marcus_, Oct 10 2020

%Y Cf. A004086, A007500.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Oct 09 2020