A372600 Least prime whose decimal representation has n distinct substrings which are also prime.

2, 13, 23, 113, 131, 137, 1013, 1031, 1279, 1237, 1973, 6173, 10139, 10193, 10391, 10739, 10937, 12739, 12379, 36137, 100937, 101693, 102931, 102397, 103913, 106319, 106937, 109379, 123479, 123973, 125791, 123719, 361973, 852937, 1006937, 1019731, 1023173, 1021973, 1024379, 1027319

Offset: 1

Author

Robert G. Wilson v, May 06 2024

Keywords

• base
• nonn

Comments

First occurrence n of pi(a(n)) in A039994: 1, 6, 9, 30, 32, 33, 170, 173, 207, 203, 298, 804, ..., .

Examples

			A039994(1) = 1, is the first occurrence of 1 which is the index of the prime 2;
A039994(6) = 2, is the first occurrence of 2 and 6 is the index of the prime 13;
A039994(9) = 3, is the first occurrence of 3 and 9 is the index of the prime 23;
A039994(30) = 4, is the first occurrence of 4 and 30 is the index of the prime 113; etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..688

Crossrefs

Cf. A039994.

Programs

Mathematica

f[p_] := Count[ PrimeQ[ Union[ FromDigits@# & /@ Rest@ Subsets[ IntegerDigits@ p]]], True]; t[_] := 0; p = 2; While[p < 10000001, a = f@ p; If[ t[a] == 0, t[a] = p]; p = NextPrime@ p]; t /@ Range@ 56