A309749 Primes p such that the base-10 concatenations (p+1)||p and (p+1)||(p+1)||p are both prime.

3, 197, 263, 281, 443, 881, 887, 947, 2111, 2129, 2237, 2699, 2741, 2897, 3251, 3539, 3821, 3881, 4049, 4451, 4523, 4787, 6257, 6389, 8609, 8741, 10163, 10193, 10247, 11027, 13187, 14591, 14897, 16193, 16901, 17027, 18797, 19319, 19379, 20147, 20681, 21563, 21647, 22073, 22259

Offset

1,1

Comments

a(n) == 5 (mod 6) for n >= 2.

Links

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

Example

a(3) = 263 is in the sequence because 263, 264263 and 264264263 are all prime.

Maple

filter:= proc(n) local v, w, q;
  if not isprime(n) then return false fi;
  v:= 10^(1+ilog10(n));
  q:= v*(n+1)+n;
  if not isprime(q) then return false fi;
  isprime((10^(1+ilog10(q))+v)*(n+1)+n)
end proc:
select(filter, [3, seq(i, i=5..100000, 6)]);

Mathematica

pcQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n+1]}, AllTrue[ {FromDigits[ Join[ idn2, idn]], FromDigits[ Join[idn2, idn2, idn]]}, PrimeQ]]; Select[Prime[Range[2500]], pcQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 11 2019 *)

Prog

(Magma) [p:p in PrimesUpTo(23000)|IsPrime(Seqint(Intseq(p) cat Intseq(p+1))) and IsPrime(Seqint(Intseq(p) cat Intseq(p+1) cat Intseq(p+1)))]; // Marius A. Burtea, Aug 27 2019

Crossrefs

Cf. A309935.

Sequence in context: A093978 A101382 A000724 * A209120 A336250 A374514

Adjacent sequences: A309746 A309747 A309748 * A309750 A309751 A309752

Keyword

nonn,base

Author

Robert Israel, Aug 26 2019

Status

approved