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

1,1

Comments

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

Links

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

Example

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.

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

Crossrefs

Cf. A039994.

Sequence in context: A285789 A090528 A094535 * A035244 A085822 A213321

Adjacent sequences: A372597 A372598 A372599 * A372601 A372602 A372603

Keyword

base,nonn,changed

Author

Robert G. Wilson v, May 06 2024

Status

approved