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

1,1

Links

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

Example

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.

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

Crossrefs

Cf. A018834, A046837.

Sequence in context: A168206 A120831 A393534 * A253254 A373730 A363347

Adjacent sequences: A385706 A385707 A385708 * A385710 A385711 A385712

Keyword

nonn,base

Author

Zhining Yang, Jul 07 2025

Status

approved