A376163 Positions of adjacent non-prime-powers (inclusive, so 1 is a prime-power) differing by 1.

4, 7, 8, 14, 15, 16, 18, 19, 22, 23, 26, 27, 29, 30, 31, 32, 35, 37, 39, 40, 43, 44, 45, 46, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 66, 67, 70, 71, 73, 74, 75, 76, 77, 78, 80, 81, 84, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 102, 103, 104, 105

Offset: 1

Author

Gus Wiseman, Sep 13 2024

Keywords

• nonn

Examples

			The non-prime-powers (inclusive) are 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, ... which increase by 1 after positions 4, 7, 8, ...
		

Crossrefs

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.

The exclusive version is a(n) - 1 = A375713.

Positions of 1's in A375735.

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

ce=Select[Range[2,100],!PrimePowerQ[#]&];
Select[Range[Length[ce]-1],ce[[#+1]]==ce[[#]]+1&]