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Minimal augmented difference between adjacent reversed prime indices of n; a(1) = 0.
10

%I #10 Jul 14 2022 17:23:18

%S 0,1,2,1,3,1,4,1,1,1,5,1,6,1,2,1,7,1,8,1,2,1,9,1,1,1,1,1,10,1,11,1,2,

%T 1,2,1,12,1,2,1,13,1,14,1,1,1,15,1,1,1,2,1,16,1,3,1,2,1,17,1,18,1,1,1,

%U 3,1,19,1,2,1,20,1,21,1,1,1,2,1,22,1,1,1

%N Minimal augmented difference between adjacent reversed prime indices of n; a(1) = 0.

%C 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 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 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.

%e The reversed prime indices of 825 are (5,3,3,2), with augmented differences (3,1,2,2), so a(825) = 1.

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t aug[y_]:=Table[If[i<Length[y],y[[i]]-y[[i+1]]+1,y[[i]]],{i,Length[y]}];

%t Table[If[n==1,0,Min@@aug[Reverse[primeMS[n]]]],{n,100}]

%Y Crossrefs found in the link are not repeated here.

%Y Positions of first appearances are A008578.

%Y Positions of 1's are 2 followed by A013929.

%Y The non-augmented maximal version is A286470, also A355526.

%Y The non-augmented version is A355524, also A355525.

%Y Row minima of A355534, which has Heinz number A325351.

%Y The maximal version is A355535.

%Y A001222 counts prime indices.

%Y A112798 lists prime indices, sum A056239.

%Y Cf. A124010, A129654, A243055, A243056, A307824, A325366, A325394, A355528, A355533, A355536.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jul 14 2022