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

7, 19, 97, 109, 151, 163, 181, 193, 547, 709, 727, 733, 991, 1039, 1093, 1279, 1447, 1453, 1567, 1621, 1657, 1669, 1699, 1723, 1867, 5077, 5179, 5209, 5281, 5323, 5419, 5503, 5563, 5581, 5653, 5821, 5857, 5881, 7057, 7207, 7219, 7333, 7351, 7507, 7537

Offset

1,1

Comments

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.

Conjecture: All these primes are of the form 6*k + 1. - Davide Rotondo, Apr 29 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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.

Maple

filter:= proc(n) local L, d, i, x;
  if not isprime(n) then return false fi;
  L:= convert(n, base, 10);
  d:= nops(L);
  x:= add(L[-i]*(10^(i-1)+10^(2*d-i)), i=1..d)+2;
  isprime(x)
end proc;
select(filter, [seq(i, i=7 .. 10^4, 6)]); # Robert Israel, Apr 29 2025

Mathematica

crpQ[n_]:=Module[{idn=IntegerDigits[n]}, PrimeQ[FromDigits[ Join[ idn, Reverse[ idn]]]+2]]; Select[Prime[Range[1000]], crpQ] (* Harvey P. Dale, Apr 28 2014 *)

Crossrefs

Subsequence of A002476.

Cf. A067087 (concatenation of n-th prime and its reverse), A088884 (with decremented rather than incremented).

Sequence in context: A363668 A245489 A084603 * A262186 A346513 A026574

Adjacent sequences: A088880 A088881 A088882 * A088884 A088885 A088886

Keyword

base,nonn

Author

Chuck Seggelin, Oct 21 2003

Status

approved