A377784 First-differences of A377783 (least nonsquarefree number > prime(n)).

0, 4, 0, 4, 4, 2, 2, 4, 8, 0, 8, 4, 0, 4, 6, 6, 3, 5, 4, 3, 5, 4, 6, 8, 6, 0, 4, 4, 4, 12, 4, 8, 0, 10, 2, 8, 4, 4, 7, 5, 4, 8, 4, 2, 2, 12, 12, 4, 4, 2, 6, 2, 10, 8, 4, 6, 2, 7, 5, 0, 10, 14, 4, 3, 5, 12, 6, 10, 2, 6, 4, 8, 7, 5, 4, 8, 8, 4, 8, 8, 3, 9, 4, 4

Offset

1,2

Comments

There are no consecutive 0's.

Does this sequence contain every positive integer > 1?

Links

Table of n, a(n) for n=1..84.

Mathematica

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

Crossrefs

Positions of 0's are A068361.

The opposite for squarefree is A378038, differences of A112925.

For prime-power instead of nonsquarefree and primes + 1 we have A377703, first-differences of A345531.

First-differences of A377783, union A378040.

The opposite is A378034 (differences of A378032), restriction of A378036 (differences A378033).

For squarefree instead of nonsquarefree we have A378037, first-differences of A112926.

Restriction of A378039 (first-differences of A120327) to the primes.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

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

A061398, A068360, A337030, A377430, A377431 count squarefree numbers between primes.

A061399, A068361, A378086 count nonsquarefree numbers between primes.

A070321 gives the greatest squarefree number up to n.

Cf. A000015, A013928, A053797, A053806, A072284, A224363.

Cf. A377047, A377048, A377049.

Cf. A378082, A378083, A378084.

Sequence in context: A031362 A378012 A198414 * A309721 A110854 A278086

Adjacent sequences: A377781 A377782 A377783 * A377785 A377786 A377787

Keyword

nonn

Author

Gus Wiseman, Nov 18 2024

Status

approved