A348667 a(n) is the index of the first 0 term in the following sequence: X(1)=1, X(i+1) = (X(i)+i) mod (n+i). a(n)=-1 if there are no zeros in the X sequence.

2, 2, 3, 19, 4, 16, 7, 5, 84, 467, 21, 6, 51, 134, 37, 75, 7, 81, 113, 16, 74, 403, 8, 52, 12, 125, 25, 163, 318, 9, 305, 31, 53, 17, 169, 14, 60, 10, 66, 36, 3500, 15, 22, 19, 42, 38, 11, 34, 113, 48, 130, 208, 994, 1033, 468, 17, 12, 53, 307, 623, 45, 173, 48

Offset: 0

Author

Alex Ratushnyak, Oct 28 2021

Keywords

• nonn

Comments

Conjecture: a(n) > 0.

Note that some terms are unexpectedly large, for example a(1059) = 62573802.

Crossrefs

Cf. A177356.

Programs

Mathematica

a[n_] := Module[{x, k = 1}, x[1] = 1; x[j_] := x[j] = Mod[x[j - 1] + j - 1, n + j - 1]; While[x[k] != 0, k++]; k]; Array[a, 63, 0] (* Amiram Eldar, Oct 29 2021 *)

PARI

a(n) = my(x=1, i=1); while(x, x = (x+i) % (n+i); i++); i; \\ Michel Marcus, Oct 29 2021

Python

for n in range(1060):
  i = x = 1
  while x:
    x = (x+i) % (n+i)
    i += 1
  print(i, end=', ')