A385709 Least prime p such that the decimal expansion of p^2 contains exactly n distinct primes as substrings.

11, 5, 23, 61, 73, 239, 487, 523, 569, 3461, 1319, 3373, 8923, 4937, 12619, 11489, 15569, 32189, 105173, 135319, 46619, 56473, 177127, 234161, 295861, 471923, 664319, 2366387, 3183613, 1092389, 3513877, 7702319, 4632077, 10666177, 13977923, 20825939, 35821939

Offset: 1

Author

Zhining Yang, Jul 07 2025

Keywords

• nonn
• base

Examples

			a(9) = 569 because 569^2 = 323761, which contains 9 distinct primes as substring:{2,3,7,23,37,61,761,3761,23761}, and no prime less than 569 has 9 solutions.
		

Links

• Zhining Yang, Table of n, a(n) for n = 1..66

Crossrefs

Cf. A018834, A046837.

Programs

Mathematica

b = Table[{}, 9]; Do[d = IntegerDigits[p^2];
 t = Union@Select[FromDigits /@ Flatten[Table[Partition[d, k, 1], {k, Length@d}], 1], PrimeQ]; c = Length@t;
 If[b[[c]] == {}, b[[c]] = {p, p^2, t, c}], {p, Prime@Range@120}]; b // Grid