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A355526 Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.

%I A355526 #7 Jul 11 2022 08:33:48
%S A355526 1,2,0,3,1,4,0,0,2,5,1,6,3,1,0,7,1,8,2,2,4,9,1,0,5,0,3,10,1,11,0,3,6,
%T A355526 1,1,12,7,4,2,13,2,14,4,1,8,15,1,0,2,5,5,16,1,2,3,6,9,17,1,18,10,2,0,
%U A355526 3,3,19,6,7,2,20,1,21,11,1,7,1,4,22,2,0,12
%N A355526 Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.
%C A355526 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.
%H A355526 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A355526 The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 4.
%t A355526 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355526 Table[If[PrimeQ[n],PrimePi[n],Max@@Differences[primeMS[n]]],{n,2,100}]
%Y A355526 Crossrefs found in the link are not repeated here.
%Y A355526 Positions of first appearances are 4 followed by A000040.
%Y A355526 Positions of 0's are A025475, minimal version A013929.
%Y A355526 Positions of 1's are 2 followed by A066312, minimal version A355527.
%Y A355526 Triangle A238710 counts m such that A056239(m) = n and a(m) = k.
%Y A355526 Prepending 0 to the prime indices gives A286469, minimal version A355528.
%Y A355526 See also A286470, minimal version A355524.
%Y A355526 The minimal version is A355525, triangle A238709.
%Y A355526 The augmented version is A355532.
%Y A355526 A001522 counts partitions with a fixed point (unproved), ranked by A352827.
%Y A355526 A287352, A355533, A355534, A355536 list the differences of prime indices.
%Y A355526 Cf. A000005, A047966, A091602, A238353, A279945, A325160, A325161, A352822, A351294, A355530.
%K A355526 nonn
%O A355526 2,2
%A A355526 _Gus Wiseman_, Jul 10 2022