A383814 Least number which satisfies the requirements of A380943 in exactly n ways.

2, 37, 373, 19937, 257931013, 4199993923

Offset: 0

Author

James C. McMahon and Robert G. Wilson v, May 29 2025

Keywords

• nonn
• base
• more

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

			See the examples in A383810 through A383813.
		

Crossrefs

Cf. A000040, A173935, A380943, A383810, A383811, A383812, A383813, 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];a[n_]:=Module[{k=1},While[f[Prime[k]]!=n,k++];Prime[k]];Array[a,4,0]