A215452 a(1)=1, a(n) = (sum of previous terms) mod (a(n-1) + n).

1, 1, 2, 4, 8, 2, 0, 2, 9, 10, 18, 27, 4, 16, 11, 7, 2, 4, 13, 9, 0, 18, 4, 4, 2, 10, 3, 5, 26, 54, 21, 32, 4, 29, 42, 14, 10, 44, 57, 44, 63, 6, 5, 10, 52, 23, 32, 44, 64, 74, 71, 33, 18, 60, 93, 29, 46, 48, 60, 84, 38, 26, 39, 46, 83, 81, 25, 59, 93, 22, 47, 24, 34, 53

Offset: 1

Author

Alex Ratushnyak, Aug 11 2012

Keywords

• nonn

Comments

Indices of 0's: 7, 21, 956, 1576, 1964, 55346, 70460, 99845, 399114, 544095, 35321849, 77073660, ...

Indices of 1's: 1, 2, 129, 193, 262, 4495, 99781, 651856, 35351437, ...

Indices such that a(n)=n: 1, 4, 9, 10, 32, 176, 266, 414, 432, 440, 858, 5953, 6030, 15146, 1408096, 3138130, 35659404, 44722350, 109021513, 790542727, ...

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A094405, A066910, A215451.

Programs

Maple

s:= proc(n) option remember; `if`(n<1, 0, s(n-1)+a(n)) end:
a:= proc(n) option remember; `if`(n=1, 1, irem(s(n-1), a(n-1)+n)) end:
seq(a(n), n=1..74);  # Alois P. Heinz, Jun 16 2025

Mathematica

nxt[{t_,n_,a_}]:={t+a,n+1,Mod[t+a,a+n+1]}; NestList[nxt,{0,1,1},80][[All,3]] (* Harvey P. Dale, Sep 01 2016 *)

Python

s = a = 1
for n in range(2,333):
    print(a, end=", ")
    a = s % (a+n)
    s += a

Formula

a(1)=1, a(n) = (a(0)+...+a(n-1)) mod (a(n-1)+n).