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A384953 First of three consecutive primes whose concatenations, both forward and backward, are primes.

%I A384953 #13 Jun 14 2025 18:41:34
%S A384953 313,359,383,449,619,787,827,907,1697,2503,2521,2857,3673,3853,4139,
%T A384953 4363,4993,5281,5527,5563,5641,5851,6037,6043,6719,7019,7477,9281,
%U A384953 10177,10459,13799,14009,15013,15511,17167,17209,19183,19423,20483,20743,21397,21407,25111
%N A384953 First of three consecutive primes whose concatenations, both forward and backward, are primes.
%H A384953 Robert Israel, <a href="/A384953/b384953.txt">Table of n, a(n) for n = 1..10000</a>
%e A384953 a(3) = 383 is a term because 383, 389 and 397 are consecutive primes and both 383389397 and 397389383 are prime.
%p A384953 rcat:= proc(L) local x,i;
%p A384953   x:= L[1];
%p A384953   for i from 2 to nops(L) do
%p A384953     x:= 10^(1+ilog10(x))*L[i] + x
%p A384953   od;
%p A384953   x
%p A384953 end proc:
%p A384953 fcat:= proc(L) local x,i;
%p A384953   x:= L[1];
%p A384953   for i from 2 to nops(L) do
%p A384953     x:= 10^(1+ilog10(L[i]))*x + L[i]
%p A384953   od;
%p A384953   x
%p A384953 end proc:
%p A384953 P:= select(isprime,[seq(i,i=3..30000,2)]):
%p A384953 J:=  select(i -> isprime(rcat(P[i..i+2])) and isprime(fcat(P[i..i+2])), [$1..nops(P)-2]):
%p A384953 P[J];
%Y A384953 Cf. A030469, A104328.
%K A384953 nonn,base
%O A384953 1,1
%A A384953 _Robert Israel_, Jun 13 2025