A383811 Primes which satisfy the requirements of A380943 in exactly two ways.

373, 1913, 3733, 6737, 7937, 11353, 13997, 19997, 23773, 24113, 29347, 31181, 31193, 31907, 34729, 37277, 38237, 41593, 47293, 59929, 71971, 72719, 73823, 74177, 79337, 79613, 82373, 83773, 83911, 88397, 100913, 111773, 111973, 118171, 118273, 118747, 132113, 132137, 139547

Offset: 1

Author

James C. McMahon and Robert G. Wilson v, May 17 2025

Keywords

• nonn
• base

Comments

The requirements of A380943 are that primes, p_n, written in decimal representation by the concatenation of primes p and q such that the concatenation of q and p also forms a prime.

Examples

			373 is a member since 373 is the 74th prime, p=3 and q=73, and the reverse concatenation is 733 which is the 130th prime. In another way, p=37 and q=3, and the reverse concatenation is 337, the 68th prime.
		

Crossrefs

Cf. A000040, A238057, A380943, A383810, A383812, A383813, A383814, A383815, A383816.

Programs

Mathematica

f[n_] := Block[{cnt = 0, id = IntegerDigits@ n, k = 1, len, p, q, qp}, len = Length@ id; While[k < len, p = Take[id, k]; q = Take[id, -len + k]; qp = FromDigits[ Join[q, p]]; If[ PrimeQ[FromDigits[p]] && PrimeQ[FromDigits[q]] && PrimeQ[qp] && IntegerLength[qp] == len, cnt++]; k++]; cnt];Select[ Prime@ Range@ 13000, f@# == 2 &]