A375713 Indices of consecutive non-prime-powers (A361102) differing by 1. Numbers k such that the k-th and (k+1)-th non-prime-powers differ by just one.

5, 8, 9, 15, 16, 17, 19, 20, 23, 24, 27, 28, 30, 31, 32, 33, 36, 38, 40, 41, 44, 45, 46, 47, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 67, 68, 71, 72, 74, 75, 76, 77, 78, 79, 81, 82, 85, 87, 88, 89, 90, 93, 94, 95, 96, 97, 98, 99, 100, 103, 104, 105, 106

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Formula

A361102(k+1) - A361102(k) = 1.

Example

The initial non-prime-powers are 1, 6, 10, 12, 14, 15, 18, 20, 21, which first increase by one after the fifth and eighth terms.

Mathematica

Join@@Position[Differences[Select[Range[100], !PrimePowerQ[#]&]], 1]

Crossrefs

The inclusive version is a(n) - 1.

For prime-powers inclusive (A000961) we have A375734, differences A373671.

For nonprime numbers (A002808) we have A375926, differences A373403.

For prime-powers exclusive (A246655) we have A375734(n+1) + 1.

First differences are A373672.

Positions of 1's in A375708.

For non-perfect-powers we have A375740.

Prime-powers inclusive:

- terms: A000961

- differences: A057820

- runs: A373675, A373673, A373674, A174965

- antiruns: A373576, A120430, A006549, A373671

Non-prime-powers inclusive:

- terms: A361102

- differences: A375708

- runs: A373678, A373676, A373677, A110969

- antiruns: A373679, A373575, A255346, A373672

A000040 lists all of the primes, differences A001223.

A007916 lists non-perfect-powers, differences A375706.

Cf. A046933, A053289, A073783, A093555, A176246, A251092, A375714.

Sequence in context: A334919 A047616 A287551 * A231065 A314576 A045221

Adjacent sequences: A375710 A375711 A375712 * A375714 A375715 A375716

Keyword

nonn

Author

Gus Wiseman, Sep 02 2024

Status

approved