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

%I A379931 #13 Jan 09 2025 19:17:42
%S A379931 2,3,5,6,7,11,12,18,20,22,25,28,33,36,45,49,50,52,55,60,63,66,68,75,
%T A379931 76,77,84,90,92,98,100,104,108,111,116,117,120,125,135,136,152,168,
%U A379931 184,188,189,216,220,222,225,228,232,244,248,250,264,270,280,296,297,300,312,328,332,338,343,351
%N A379931 Numbers whose maximum exponent in their prime factorization is the number of runs in their base-10 representation.
%C A379931 Numbers k such that A051903(k) = A043562(k).
%C A379931 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.
%H A379931 Robert Israel, <a href="/A379931/b379931.txt">Table of n, a(n) for n = 1..10000</a>
%e A379931 a(10) = 22 is a term because 22 = 2 * 11 has maximum exponent 1, and one run in its base 10 representation.
%p A379931 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:
%p A379931 select(filter, [$1..1000]);
%t A379931 A379931Q[n_] := n > 1 && Max[FactorInteger[n][[All, 2]]] == Length[Split[IntegerDigits[n]]];
%t A379931 Select[Range[400], A379931Q] (* _Paolo Xausa_, Jan 08 2025 *)
%Y A379931 Cf. A043562, A051903, A379929, A379930.
%K A379931 nonn,base
%O A379931 1,1
%A A379931 _Robert Israel_, Jan 06 2025