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

Author

Gus Wiseman, Sep 02 2024

Keywords

• nonn

Examples

			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.
		

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.

Programs

Mathematica

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

Formula

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