A379931 Numbers whose maximum exponent in their prime factorization is the number of runs in their base-10 representation.

2, 3, 5, 6, 7, 11, 12, 18, 20, 22, 25, 28, 33, 36, 45, 49, 50, 52, 55, 60, 63, 66, 68, 75, 76, 77, 84, 90, 92, 98, 100, 104, 108, 111, 116, 117, 120, 125, 135, 136, 152, 168, 184, 188, 189, 216, 220, 222, 225, 228, 232, 244, 248, 250, 264, 270, 280, 296, 297, 300, 312, 328, 332, 338, 343, 351

Offset: 1

Author

Robert Israel, Jan 06 2025

Keywords

• nonn
• base

Comments

Numbers k such that A051903(k) = A043562(k).

If k has r runs, maximum exponent m <= r, and is coprime to 10, then 10^(r+1) * k is a term. Therefore this sequence is infinite.

Examples

			a(10) = 22 is a term because 22 = 2 * 11 has maximum exponent 1, and one run in its base 10 representation.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A043562, A051903, A379929, A379930.

Programs

Maple

filter:= proc(n) local L; L:= convert(n, base, 10); nops(L) - numboccur(0, L[2..-1]-L[1..-2]) = max(ifactors(n)[2][..,2]) end proc:
select(filter, [$1..1000]);

Mathematica

A379931Q[n_] := n > 1 && Max[FactorInteger[n][[All, 2]]] == Length[Split[IntegerDigits[n]]];
Select[Range[400], A379931Q] (* Paolo Xausa, Jan 08 2025 *)