A378087 First-differences of A067535 (least positive integer >= n that is squarefree).

1, 1, 2, 0, 1, 1, 3, 0, 0, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 3, 0, 0, 3, 0, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 3, 0, 0, 1, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 3, 0, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 3, 0, 0, 1, 1, 3, 0, 0, 1, 2, 0, 1, 1, 2

Offset: 1

Author

Gus Wiseman, Nov 20 2024

Keywords

• nonn

Comments

Does this contain all nonnegative integers? The positions of first appearances begin: 4, 1, 3, 7, 47, 241, 843, 22019, 217069, ...

Crossrefs

Ones are A007674.

Zeros are A013929, complement A005117.

Positions of first appearances are A020754 (except first term) = A045882 - 1.

First-differences of A067535.

Twos are A280892.

For prime-powers we have A377780, differences of A000015.

The nonsquarefree opposite is A378036, differences of A378033.

The restriction to primes + 1 is A378037 (opposite A378038), differences of A112926.

For nonsquarefree numbers we have A378039, see A377783, A377784, A378040.

The opposite is A378085, differences of A070321.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

A061398 counts squarefree numbers between primes, zeros A068360.

A061399 counts nonsquarefree numbers between primes, zeros A068361.

Cf. A005117, A007675, A068781, A073247, A073248, A378084.

Cf. A013928, A053797, A053806, A072284, A120327, A224363.

Programs

Mathematica

Differences[Table[NestWhile[#+1&,n,#>1&&!SquareFreeQ[#]&],{n,100}]]