cp's OEIS Frontend

A355528 Minimal difference between adjacent 0-prepended prime indices of n > 1.

%I A355528 #9 Jul 13 2022 20:37:09
%S A355528 1,2,0,3,1,4,0,0,1,5,0,6,1,1,0,7,0,8,0,2,1,9,0,0,1,0,0,10,1,11,0,2,1,
%T A355528 1,0,12,1,2,0,13,1,14,0,0,1,15,0,0,0,2,0,16,0,2,0,2,1,17,0,18,1,0,0,3,
%U A355528 1,19,0,2,1,20,0,21,1,0,0,1,1,22,0,0,1,23
%N A355528 Minimal difference between adjacent 0-prepended prime indices of n > 1.
%C A355528 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 A355528 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.
%e A355528 The 0-prepended prime indices of 9842 are {0,1,4,8,12}, with differences (1,3,4,4), so a(9842) = 1.
%t A355528 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355528 Table[Min@@Differences[Prepend[primeMS[n],0]],{n,2,100}]
%Y A355528 Crossrefs found in the link are not repeated here.
%Y A355528 Positions of first appearances are 4 followed by A000040.
%Y A355528 Positions of positive terms are A005117, complement A013929.
%Y A355528 A similar statistic is counted by A238353.
%Y A355528 The maximal version is A286469, without prepending A355526.
%Y A355528 Without prepending we have A355524 or A355525.
%Y A355528 Positions of ones are A355530.
%Y A355528 A001522 counts partitions with a fixed point (unproved), ranked by A352827.
%Y A355528 A112798 lists prime indices, with sum A056239.
%Y A355528 A287352, A355533, A355534, A355536 list the differences of prime indices.
%Y A355528 Cf. A064428, A066312, A091602, A120944, A238354, A286470, A325161, A352822, A355527, A355531, A355532.
%K A355528 nonn
%O A355528 2,2
%A A355528 _Gus Wiseman_, Jul 10 2022