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A355524 Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.

%I A355524 #6 Jul 11 2022 08:33:35
%S A355524 0,0,0,0,1,0,0,0,2,0,0,0,3,1,0,0,0,0,0,2,4,0,0,0,5,0,0,0,1,0,0,3,6,1,
%T A355524 0,0,7,4,0,0,1,0,0,0,8,0,0,0,0,5,0,0,0,2,0,6,9,0,0,0,10,0,0,3,1,0,0,7,
%U A355524 1,0,0,0,11,0,0,1,1,0,0,0,12,0,0,4,13,8
%N A355524 Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.
%C A355524 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 A355524 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A355524 The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.
%t A355524 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355524 Table[If[PrimeQ[n],0,Min@@Differences[primeMS[n]]],{n,2,100}]
%Y A355524 Crossrefs found in the link are not repeated here.
%Y A355524 Positions of first appearances are A077017 w/o the first term.
%Y A355524 Positions of terms > 0 are A120944.
%Y A355524 Positions of zeros are A130091.
%Y A355524 Triangle A238353 counts m such that A056239(m) = n and a(m) = k.
%Y A355524 For maximal difference we have A286470 or A355526.
%Y A355524 Positions of terms > 1 are A325161.
%Y A355524 If singletons (k) have minimal difference k we get A355525.
%Y A355524 Positions of 1's are A355527.
%Y A355524 Prepending 0 to the prime indices gives A355528.
%Y A355524 A115720 and A115994 count partitions by their Durfee square.
%Y A355524 A287352, A355533, A355534, A355536 list the differences of prime indices.
%Y A355524 Cf. A000005, A066312, A238354, A238710, A286469, A351294, A352822, A355530, A355531, A355532.
%K A355524 nonn
%O A355524 2,9
%A A355524 _Gus Wiseman_, Jul 10 2022