A355524 - OEIS

A355524

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

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, 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, 1, 0, 0, 0, 11, 0, 0, 1, 1, 0, 0, 0, 12, 0, 0, 4, 13, 8

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OFFSET

2,9

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..87.

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], 0, Min@@Differences[primeMS[n]]], {n, 2, 100}]

CROSSREFS

Crossrefs found in the link are not repeated here.

Positions of first appearances are A077017 w/o the first term.

Positions of terms > 0 are A120944.

Positions of zeros are A130091.

Triangle A238353 counts m such that A056239(m) = n and a(m) = k.

For maximal difference we have A286470 or A355526.

Positions of terms > 1 are A325161.

If singletons (k) have minimal difference k we get A355525.

Positions of 1's are A355527.

Prepending 0 to the prime indices gives A355528.

A115720 and A115994 count partitions by their Durfee square.

A287352, A355533, A355534, A355536 list the differences of prime indices.

Cf. A000005, A066312, A238354, A238710, A286469, A351294, A352822, A355530, A355531, A355532.

Sequence in context: A257685 A347233 A327172 * A113503 A082507 A132349

Adjacent sequences: A355521 A355522 A355523 * A355525 A355526 A355527

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 10 2022

STATUS

approved