cp's OEIS Frontend

A384906 Number of maximal anti-runs of consecutive parts not increasing by 1 in the prime indices of n (with multiplicity).

%I A384906 #11 Jul 12 2025 08:37:02
%S A384906 0,1,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,
%T A384906 2,2,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,1,
%U A384906 1,2,1,2,1,1,2,1,2,2,1,1,1,1,1,2,1,1,1
%N A384906 Number of maximal anti-runs of consecutive parts not increasing by 1 in the prime indices of n (with multiplicity).
%C A384906 First differs from A300820 at a(462) = 3, A300820(462) = 2.
%C A384906 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 A384906 The prime indices of 462 are {1,2,4,5}, with maximal anti-runs ((1),(2,4),(5)), so a(462) = 3.
%t A384906 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A384906 Table[Length[Split[prix[n],#2!=#1+1&]],{n,100}]
%Y A384906 For the strict case we have A356228.
%Y A384906 For binary instead of prime indices we have A384890 (for runs A069010).
%Y A384906 For runs instead of anti-runs we have A385213.
%Y A384906 A034839 counts subsets by number of maximal runs, for strict partitions A116674.
%Y A384906 A055396 gives least prime index, greatest A061395.
%Y A384906 A056239 adds up prime indices, row sums of A112798.
%Y A384906 A384877 gives lengths of maximal anti-runs in binary indices, firsts A384878.
%Y A384906 Cf. A130091, A245562, A268193, A300820, A351202, A356607, A382525, A384177, A384321, A384893.
%K A384906 nonn
%O A384906 1,6
%A A384906 _Gus Wiseman_, Jun 22 2025