A377431 Numbers k such that there is at least one squarefree number between prime(k)+1 and prime(k+1)-1.

3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

Primes 4 and 5 are 7 and 11, and the interval (8,9,10) contains 10, which is squarefree, so 4 is in the sequence.

Mathematica

Select[Range[100], Length[Select[Range[Prime[#]+1, Prime[#+1]-1], SquareFreeQ]]>=1&]

Crossrefs

These are the positive positions in A061398, or terms >= 2 in A373198.

The complement (no squarefree numbers) is A068360.

For prime-power instead of squarefree we have A377057, strict version A377287.

For exactly one squarefree number we have A377430.

A000040 lists the primes, differences A001223, seconds A036263.

A002808 lists the composites, complement A008578.

A005117 lists the squarefree numbers, complement A013929.

A377038 gives k-differences of squarefree numbers.

Cf. A007674, A013603, A029707, A036378, A046933, A072284, A076259, A077641, A077643, A075526, A078147, A112925, A112926, A120992, A293697.

Sequence in context: A199015 A196098 A099356 * A325209 A121543 A080702

Adjacent sequences: A377428 A377429 A377430 * A377432 A377433 A377434

Keyword

nonn

Author

Gus Wiseman, Oct 29 2024

Status

approved