A355531 Minimal augmented difference between adjacent reversed prime indices of n; a(1) = 0.

0, 1, 2, 1, 3, 1, 4, 1, 1, 1, 5, 1, 6, 1, 2, 1, 7, 1, 8, 1, 2, 1, 9, 1, 1, 1, 1, 1, 10, 1, 11, 1, 2, 1, 2, 1, 12, 1, 2, 1, 13, 1, 14, 1, 1, 1, 15, 1, 1, 1, 2, 1, 16, 1, 3, 1, 2, 1, 17, 1, 18, 1, 1, 1, 3, 1, 19, 1, 2, 1, 20, 1, 21, 1, 1, 1, 2, 1, 22, 1, 1, 1

Offset

1,3

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.

The augmented differences aug(q) of a (usually weakly decreasing) sequence q of length k are given by aug(q)_i = q_i - q_{i+1} + 1 if i < k and aug(q)_k = q_k. For example, we have aug(6,5,5,3,3,3) = (2,1,3,1,1,3).

Links

Table of n, a(n) for n=1..82.

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

Example

The reversed prime indices of 825 are (5,3,3,2), with augmented differences (3,1,2,2), so a(825) = 1.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
aug[y_]:=Table[If[i<Length[y], y[[i]]-y[[i+1]]+1, y[[i]]], {i, Length[y]}];
Table[If[n==1, 0, Min@@aug[Reverse[primeMS[n]]]], {n, 100}]

Crossrefs

Crossrefs found in the link are not repeated here.

Positions of first appearances are A008578.

Positions of 1's are 2 followed by A013929.

The non-augmented maximal version is A286470, also A355526.

The non-augmented version is A355524, also A355525.

Row minima of A355534, which has Heinz number A325351.

The maximal version is A355535.

A001222 counts prime indices.

A112798 lists prime indices, sum A056239.

Cf. A124010, A129654, A243055, A243056, A307824, A325366, A325394, A355528, A355533, A355536.

Sequence in context: A335105 A350597 A325252 * A234809 A135591 A114897

Adjacent sequences: A355528 A355529 A355530 * A355532 A355533 A355534

Keyword

nonn

Author

Gus Wiseman, Jul 14 2022

Status

approved