A383812 Primes which satisfy the requirements of A380943 in exactly three ways.

19937, 103997, 377477, 577937, 738677, 739397, 877937, 2116397, 3110273, 3314513, 3343337, 3634313, 3833359, 5935393, 7147397, 7276337, 7511033, 7699157, 7723337, 11816911, 14713613, 19132213, 19132693, 19998779, 22739317, 23201359, 31189757, 31614377, 31669931, 31687151

Offset

1,1

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.

The number of terms <= 10^k beginning with k=1: 0, 0, 0, 0, 1, 7, 19, 70, 299, 1872, ..., .

Links

Table of n, a(n) for n=1..30.

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@ 1980000, f@# == 3 &]

Crossrefs

Cf. A000040, A238499, A380943, A383810, A383811, A383813, A383814, A383815, A383816.

Sequence in context: A263298 A237564 A171353 * A175590 A324594 A203045

Adjacent sequences: A383809 A383810 A383811 * A383813 A383814 A383815

Keyword

nonn,base

Author

James C. McMahon and Robert G. Wilson v, May 18 2025

Status

approved