A330256 - OEIS

A330256

a(0) = 0; for n > 0, a(n) = n - a((Sum_{k=0..n-1} a(k)) mod n).

0, 1, 1, 2, 4, 3, 3, 7, 5, 4, 10, 4, 7, 6, 13, 5, 12, 16, 12, 18, 14, 21, 9, 11, 10, 14, 22, 15, 14, 28, 9, 10, 23, 31, 24, 33, 22, 15, 37, 24, 16, 40, 14, 34, 37, 36, 43, 23, 34, 42, 13, 18, 37, 50, 17, 18, 32, 40, 40, 19, 46, 57, 39, 59, 30, 15, 32, 21, 11, 32, 40, 65, 32, 62, 41, 58, 63, 60

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

OFFSET

0,4

LINKS

Samuel B. Reid, Table of n, a(n) for n = 0..10000

Samuel B. Reid, Colored plot of one billion terms. This plot is normalized by column. Within each column, density corresponds, in a linear fashion, to this spectrum.

Samuel B. Reid, Distribution, between 0 and n, of the first billion terms

EXAMPLE

a(1) = 1 - a(0 mod 1) = 1.

a(2) = 2 - a((0+1) mod 2) = 1.

a(3) = 3 - a((0+1+1) mod 3) = 2.

a(4) = 4 - a((0+1+1+2) mod 4) = 4.

MATHEMATICA

a[0] = 0; a[n_] := a[n] = n - a[Mod[Sum[a[k], {k, 0, n - 1}], n]]; Array[a, 100, 0] (* Amiram Eldar, Dec 07 2019 *)

PROG

(PARI) s=0; for (n=1, #(a=vector(78)), print1 (a[n]=if (n==1, 0, (n-1)-a[1+(s%(n-1))])", "); s+=a[n]) \\ Rémy Sigrist, Dec 08 2019

CROSSREFS

Cf. A330249, A066910.