A068627 a(0) = 0, a(n) = a(n-1) + n if n does not divide a(n-1). a(n) = a(n-1) - n if n divides a(n-1). a(n) = n if a(n-1) = 0.

0, 1, 3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 48, 61, 75, 60, 76, 93, 111, 130, 150, 171, 193, 216, 192, 217, 243, 216, 244, 273, 303, 334, 366, 399, 433, 468, 432, 469, 507, 468, 508, 549, 591, 634, 678, 723, 769, 816, 768, 817, 867, 816, 868, 921, 975, 1030, 1086

Offset

0,3

Comments

The sequence is not monotonically increasing but has an increasing trend with some nodes i.e. numbers occurring twice in the sequence like 60 etc. Are there infinitely many nodes in the sequence.?

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

Since 12 divides a(11)=60, a(12) = 60 - 12 = 48.
Since 13 does not divide a(12)=48, a(13) = 48 + 13 = 61.

Mathematica

nxt[{n_, a_}]:={n+1, Which[a==0, n+1, Divisible[a, n+1], a-(n+1), True, a+n+1]}; NestList[nxt, {0, 0}, 60][[All, 2]] (* Harvey P. Dale, Jun 29 2021 *)

Prog

(PARI) lista(nn) = {preca = 0; for (n=1, nn, print1(preca, ", "); if (preca == 0, nexta = n, if (preca % n, nexta = preca + n, nexta = preca - n); ); preca = nexta; ); } \\ Michel Marcus, Jan 23 2014

Crossrefs

Cf. A068626.

Sequence in context: A068630 A309764 A079406 * A357884 A074171 A180657

Adjacent sequences: A068624 A068625 A068626 * A068628 A068629 A068630

Keyword

easy,nonn

Author

Amarnath Murthy, Feb 26 2002

Status

approved