A375927 - OEIS

A375927

Numbers k such that A005117(k+1) - A005117(k) = 1. In other words, the k-th squarefree number is 1 less than the next.

1, 2, 4, 5, 7, 9, 10, 14, 15, 18, 19, 21, 22, 24, 25, 27, 28, 30, 35, 36, 38, 40, 41, 43, 44, 46, 48, 49, 51, 53, 54, 58, 59, 62, 63, 65, 66, 68, 69, 71, 72, 74, 76, 79, 80, 82, 84, 85, 87, 88, 90, 94, 96, 97, 101, 102, 105, 107, 108, 110, 111, 113, 114, 116

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The asymptotic density of this sequence is Product_{p prime} (1 - 1/(p^2-1)) = 0.53071182... (A065469). - Amiram Eldar, Sep 15 2024

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The squarefree numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ... which first increase by one after terms 1, 2, 4, 5, ...

MATHEMATICA

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

PROG

(PARI) lista(kmax) = {my(is1 = 1, is2, c = 1); for(k = 2, kmax, is2 = issquarefree(k); if(is2, c++); if(is1 && is2, print1(c-1, ", ")); is1 = is2); } \\ Amiram Eldar, Sep 15 2024

CROSSREFS

Positions of 1's in A076259.

For prime-powers (A246655) we have A375734.

First differences are A373127.

For nonsquarefree instead of squarefree we have A375709.

For nonprime numbers we have A375926, differences A373403.

For composite numbers we have A375929.

The complement is A375930, differences A120992.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.

A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

Cf. A007674, A061399, A065469, A072284, A110969, A294242, A373409, A373410, A373573.

Sequence in context: A360531 A050731 A295579 * A098794 A256228 A114055

Adjacent sequences: A375924 A375925 A375926 * A375928 A375929 A375930

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 12 2024

STATUS

approved