A352641 For any n > 0, let E_n be the variant of Van Eck's sequence where values are taken mod n; if E_n is eventually periodic, then a(n) is the length of its transient part; otherwise a(n) = -1.

0, 5, 6, 42, 8, 69, 42, 92, 252, 159, 120, 164, 462, 472, 305, 713, 118, 2073, 495, 99, 172, 419, 2189, 305, 518, 970, 601, 1174, 1007, 1209, 6202, 331, 2928, 499, 2118, 416, 3621, 3921, 302, 3042, 50, 25744, 5079, 1882, 5535, 2216, 1492, 4845, 274, 889, 1571

Offset

1,2

Comments

For any n > 0: E_n(1) = 0, and for any k > 0, if E_n(m) = E_n(k) for some m < k, take the largest such m and set E_n(k+1) = (k-m) mod n; otherwise E_n(k+1) = 0.

Note that in general, E_n(k) <> A181391(k) mod n.

For n <= 10000:

- E_n is always eventually periodic,

- except for n = 1, 3 and 4, E_n is eventually constant (with value 1).

Is E_n eventually periodic for all n?

Links

Table of n, a(n) for n=1..51.

Rémy Sigrist, C program

Example

For n = 3:
- E_3 is eventually 7-periodic:
          0 0 1 0 2 0 (2 2 1 0 1 2 1)*
- the transient part has 6 terms,
- so a(3) = 6.

Prog

(C) See Links section.

Crossrefs

Cf. A181391.

Sequence in context: A137254 A262308 A355137 * A299168 A219516 A273050

Adjacent sequences: A352638 A352639 A352640 * A352642 A352643 A352644

Keyword

nonn

Author

Rémy Sigrist, Mar 25 2022

Status

approved