A383810 Primes which satisfy the requirements of A380943 in more than one way.

373, 1913, 3733, 6737, 7937, 11353, 13997, 19937, 19997, 23773, 24113, 29347, 31181, 31193, 31907, 34729, 37277, 38237, 41593, 47293, 59929, 71971, 72719, 73823, 74177, 79337, 79613, 82373, 83773, 83911, 88397, 100913, 103997

Offset

1,1

Comments

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

The number of terms <= 10^k beginning with k=1: 0, 0, 1, 5, 31, 285, 930, 5625, 28137, 205416, ....

Links

Table of n, a(n) for n=1..33.

Example

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.

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@ 10000, f@# > 1 &]

Crossrefs

Cf. A000040, A380943, A383811, A383812, A383813, A383814, A383815, A383816.

Sequence in context: A133559 A229499 A023313 * A383811 A213301 A213300

Adjacent sequences: A383807 A383808 A383809 * A383811 A383812 A383813

Keyword

base,nonn

Author

James C. McMahon and Robert G. Wilson v, May 11 2025

Status

approved