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A355532 Maximal augmented difference between adjacent reversed prime indices of n; a(1) = 0.

%I A355532 #8 Jul 14 2022 17:23:23
%S A355532 0,1,2,1,3,2,4,1,2,3,5,2,6,4,2,1,7,2,8,3,3,5,9,2,3,6,2,4,10,2,11,1,4,
%T A355532 7,3,2,12,8,5,3,13,3,14,5,2,9,15,2,4,3,6,6,16,2,3,4,7,10,17,2,18,11,3,
%U A355532 1,4,4,19,7,8,3,20,2,21,12,2,8,4,5,22,3,2
%N A355532 Maximal augmented difference between adjacent reversed prime indices of n; a(1) = 0.
%C A355532 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.
%C A355532 The augmented differences aug(q) of a (usually weakly decreasing) sequence q of length k are given by aug(q)_i = q_i - q_{i+1} + 1 if i < k and aug(q)_k = q_k. For example, we have aug(6,5,5,3,3,3) = (2,1,3,1,1,3).
%H A355532 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.
%e A355532 The reversed prime indices of 825 are (5,3,3,2), with augmented differences (3,1,2,2), so a(825) = 3.
%t A355532 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355532 aug[y_]:=Table[If[i<Length[y],y[[i]]-y[[i+1]]+1,y[[i]]],{i,Length[y]}];
%t A355532 Table[If[n==1,0,Max@@aug[Reverse[primeMS[n]]]],{n,100}]
%Y A355532 Crossrefs found in the link are not repeated here.
%Y A355532 Prepending 1 to the positions of 1's gives A000079.
%Y A355532 Positions of first appearances are A008578.
%Y A355532 Positions of 2's are A065119.
%Y A355532 The non-augmented version is A286470, also A355526.
%Y A355532 The non-augmented minimal version is A355524, also A355525.
%Y A355532 The minimal version is A355531.
%Y A355532 Row maxima of A355534, which has Heinz number A325351.
%Y A355532 A001222 counts prime indices, distinct A001221.
%Y A355532 A112798 lists prime indices, sum A056239.
%Y A355532 Cf. A066312, A124010, A129654, A243055, A243056, A307824, A325366, A325394, A355533, A355536.
%K A355532 nonn
%O A355532 1,3
%A A355532 _Gus Wiseman_, Jul 14 2022