cp's OEIS Frontend

A385213 Number of maximal runs of consecutive parts increasing by 1 in the prime indices of n (with multiplicity).

%I A385213 #6 Jun 22 2025 14:37:42
%S A385213 0,1,1,2,1,1,1,3,2,2,1,2,1,2,1,4,1,2,1,3,2,2,1,3,2,2,3,3,1,1,1,5,2,2,
%T A385213 1,3,1,2,2,4,1,2,1,3,2,2,1,4,2,3,2,3,1,3,2,4,2,2,1,2,1,2,3,6,2,2,1,3,
%U A385213 2,2,1,4,1,2,2,3,1,2,1,5,4,2,1,3,2,2,2
%N A385213 Number of maximal runs of consecutive parts increasing by 1 in the prime indices of n (with multiplicity).
%C A385213 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A385213 The prime indices of 24 are {1,1,1,2}, with maximal runs ((1),(1),(1,2)), so a(24) = 3.
%t A385213 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A385213 Table[Length[Split[prix[n],#2==#1+1&]],{n,100}]
%Y A385213 Positions of first appearances are A000079.
%Y A385213 For binary instead of prime indices we have A069010 (for anti-runs A384890).
%Y A385213 For anti-runs instead of runs we have A384906.
%Y A385213 A034839 counts subsets by number of maximal runs, for strict partitions A116674.
%Y A385213 A055396 gives least prime index, greatest A061395.
%Y A385213 A056239 adds up prime indices, row sums of A112798.
%Y A385213 A384877 gives lengths of maximal anti-runs in binary indices, firsts A384878.
%Y A385213 Cf. A002110, A048767, A130091, A300820, A356606, A351202, A382525, A384893.
%K A385213 nonn
%O A385213 1,4
%A A385213 _Gus Wiseman_, Jun 22 2025