A379931 - OEIS

%I #13 Jan 09 2025 19:17:42

%S 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 76,77,84,90,92,98,100,104,108,111,116,117,120,125,135,136,152,168,

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

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

%C 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 Robert Israel, <a href="/A379931/b379931.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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 select(filter, [$1..1000]);

%t A379931Q[n_] := n > 1 && Max[FactorInteger[n][[All, 2]]] == Length[Split[IntegerDigits[n]]];

%t Select[Range[400], A379931Q] (* _Paolo Xausa_, Jan 08 2025 *)

%Y Cf. A043562, A051903, A379929, A379930.

%K nonn,base

%O 1,1

%A _Robert Israel_, Jan 06 2025