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

Author

Amarnath Murthy, Feb 26 2002

Keywords

• easy
• nonn

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?

Examples

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

Links

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

Crossrefs

Cf. A068626.

Programs

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 *)

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