A383812 - OEIS

%I #10 May 27 2025 23:44:34

%S 19937,103997,377477,577937,738677,739397,877937,2116397,3110273,

%T 3314513,3343337,3634313,3833359,5935393,7147397,7276337,7511033,

%U 7699157,7723337,11816911,14713613,19132213,19132693,19998779,22739317,23201359,31189757,31614377,31669931,31687151

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

%C 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.

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

%t 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 &]

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

%K nonn,base

%O 1,1

%A _James C. McMahon_ and _Robert G. Wilson v_, May 18 2025