A131663 Numbers k such that either k or k+1 is divisible by the numbers from 1 to 10.

720, 1799, 2519, 2520, 3240, 4319, 5039, 5040, 5760, 6839, 7559, 7560, 8280, 9359, 10079, 10080, 10800, 11879, 12599, 12600, 13320, 14399, 15119, 15120, 15840, 16919, 17639, 17640, 18360, 19439, 20159, 20160, 20880, 21959, 22679, 22680, 23400, 24479, 25199, 25200, 25920

Offset

1,1

Comments

Also numbers k such that 2520 | k*(k+1). - David A. Corneth, May 06 2021

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1001 terms from Harvey P. Dale)

Formula

a(n) = 2520 + a(n-4), n >= 5. - David A. Corneth, May 06 2021

Example

720 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10; while 721 is divisible by 7.

Mathematica

Select[Range[30000], Mod[ #, 8]*Mod[ # + 1, 8] == 0 && Mod[ #, 9]*Mod[ # + 1, 9] == 0 && Mod[ #, 5]*Mod[ # + 1, 5] == 0 && Mod[ #, 7]*Mod[ # + 1, 7] == 0 && Mod[ #, 8]*Mod[ # + 1, 8] == 0 && Mod[ #, 6]*Mod[ # + 1, 6] == 0 && Mod[ #, 10]*Mod[ # + 1, 10] == 0 &]
Select[Range[23000], Take[Union[Join[Divisors[#], Divisors[#+1]]], 10] == Range[ 10]&]// Quiet (* Harvey P. Dale, Jul 03 2020 *)

Prog

(PARI) first(n) = { my(res = List([720, 1799, 2519, 2520])); for(i = 5, n, listput(res, res[i-4]+2520)); res } \\ David A. Corneth, May 06 2021

Crossrefs

Cf. A002378.

Sequence in context: A067808 A302127 A291804 * A090392 A253734 A112530

Adjacent sequences: A131660 A131661 A131662 * A131664 A131665 A131666

Keyword

nonn,easy

Author

Tanya Khovanova, Sep 13 2007

Extensions

Offset changed to 1 by David A. Corneth, May 06 2021

Status

approved