A355525 - OEIS

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A355525

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

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, 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, 3, 1, 19, 0, 7, 1, 20, 0, 21, 11, 0, 0, 1, 1, 22, 0, 0, 12

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OFFSET

2,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=2..82.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

EXAMPLE

The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.

MATHEMATICA

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

Table[If[PrimeQ[n], PrimePi[n], Min@@Differences[primeMS[n]]], {n, 2, 100}]

CROSSREFS

Crossrefs found in the link are not repeated here.

Positions of first appearances are 4 followed by A000040.

Positions of 0's are A013929, see also A130091.

Triangle A238709 counts m such that A056239(m) = n and a(m) = k.

For maximal instead of minimal difference we have A286470.

Positions of terms > 1 are A325160, also A325161.