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A088883 Primes which when concatenated with their reverse and incremented by 2 yield a new prime.

%I A088883 #21 Jun 08 2025 16:15:42
%S A088883 7,19,97,109,151,163,181,193,547,709,727,733,991,1039,1093,1279,1447,
%T A088883 1453,1567,1621,1657,1669,1699,1723,1867,5077,5179,5209,5281,5323,
%U A088883 5419,5503,5563,5581,5653,5821,5857,5881,7057,7207,7219,7333,7351,7507,7537
%N A088883 Primes which when concatenated with their reverse and incremented by 2 yield a new prime.
%C A088883 It appears that if concat(p,reverse(p))+2 is prime, then concat(p,reverse(p))-2 is not and vice versa. This was tested for the first 60000 primes.
%C A088883 Conjecture: All these primes are of the form 6*k + 1. - _Davide Rotondo_, Apr 29 2025
%H A088883 Harvey P. Dale, <a href="/A088883/b088883.txt">Table of n, a(n) for n = 1..1000</a>
%e A088883 109 is a term because (i) 109 is prime and (ii) when 109 is concatenated with its reverse (901) + 2, the result (109903) is prime.
%p A088883 filter:= proc(n) local L,d,i,x;
%p A088883   if not isprime(n) then return false fi;
%p A088883   L:= convert(n,base,10);
%p A088883   d:= nops(L);
%p A088883   x:= add(L[-i]*(10^(i-1)+10^(2*d-i)),i=1..d)+2;
%p A088883   isprime(x)
%p A088883 end proc;
%p A088883 select(filter, [seq(i,i=7 .. 10^4,6)]); # _Robert Israel_, Apr 29 2025
%t A088883 crpQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[FromDigits[ Join[ idn, Reverse[ idn]]]+2]]; Select[Prime[Range[1000]],crpQ] (* _Harvey P. Dale_, Apr 28 2014 *)
%Y A088883 Subsequence of A002476.
%Y A088883 Cf. A067087 (concatenation of n-th prime and its reverse), A088884 (with decremented rather than incremented).
%K A088883 base,nonn
%O A088883 1,1
%A A088883 _Chuck Seggelin_, Oct 21 2003