cp's OEIS Frontend

A355525 Minimal difference between adjacent prime indices of n, or k if n is the k-th prime.

%I A355525 #8 Jul 11 2022 08:33:43
%S A355525 1,2,0,3,1,4,0,0,2,5,0,6,3,1,0,7,0,8,0,2,4,9,0,0,5,0,0,10,1,11,0,3,6,
%T A355525 1,0,12,7,4,0,13,1,14,0,0,8,15,0,0,0,5,0,16,0,2,0,6,9,17,0,18,10,0,0,
%U A355525 3,1,19,0,7,1,20,0,21,11,0,0,1,1,22,0,0,12
%N A355525 Minimal difference between adjacent prime indices of n, or k if n is the k-th prime.
%C A355525 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 A355525 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A355525 The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.
%t A355525 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355525 Table[If[PrimeQ[n],PrimePi[n],Min@@Differences[primeMS[n]]],{n,2,100}]
%Y A355525 Crossrefs found in the link are not repeated here.
%Y A355525 Positions of first appearances are 4 followed by A000040.
%Y A355525 Positions of 0's are A013929, see also A130091.
%Y A355525 Triangle A238709 counts m such that A056239(m) = n and a(m) = k.
%Y A355525 For maximal instead of minimal difference we have A286470.
%Y A355525 Positions of terms > 1 are A325160, also A325161.
%Y A355525 See also A355524, A355528.
%Y A355525 Positions of 1's are A355527.
%Y A355525 A001522 counts partitions with a fixed point (unproved), ranked by A352827.
%Y A355525 A238352 counts partitions by fixed points, rank statistic A352822.
%Y A355525 A287352, A355533, A355534, A355536 list the differences of prime indices.
%Y A355525 Cf. A066312, A120944, A238353, A279945, A286469, A325351, A325352, A351294, A355526, A355530, A355531, A355532.
%K A355525 nonn
%O A355525 2,2
%A A355525 _Gus Wiseman_, Jul 10 2022