A330411 a(n) is the index of the first 0 term in the rumor sequence with initial 0th term 1 and parameters b = 3 and n.

2, 1, 3, 5, 4, 24, 2, 22, 21, 20, 19, 6, 17, 16, 15, 14, 4, 6, 20, 22, 99, 8, 97, 3, 95, 94, 93, 92, 13, 393, 89, 391, 9, 389, 85, 84, 83, 82, 384, 80, 382, 60, 59, 58, 75, 377, 376, 375, 53, 373, 372, 68, 370, 66, 368, 796, 24, 365, 793, 363, 362, 361, 789, 788, 787, 786, 14, 784

Offset

1,1

Comments

"A rumor sequence (running modulus recurrence sequence) is defined as follows: fix integer parameters b > 1 and n > 0. Set z[0] = any integer, and, for k > 0, define z[k] to be the least nonnegative residue of b*z[k-1] modulo (k+n). The rumor sequence conjecture states that all such rumor sequences are eventually 0." [Copied from the comments for A177356]

Links

Table of n, a(n) for n=1..68.

B. Dearden, J. Iiams, and J. Metzger, Rumor Arrays, J. Integer Seq. 16 (2013), #13.9.3.

B. Dearden and J. Metzger, Running Modulus Recursions, J. Integer Seq. 13(1) (2010), #10.1.6.

Formula

a(n) = inf{m > 0 | z[0] = 1, z[m] = 0, and z[k] = (3*z[k-1] mod (k + n)) for k = 1..m}.

Example

For n = 1, we have z[0] = 1, z[1] = 1, and z[2] = 0, so a(1) = 2.
For n = 2, we have z[0] = 1 and z[1] = 0, so a(2) = 1.
For n = 3, we have z[0] = 1, z[1] = 3, z[2] = 4, and z[3] = 0, so a(3) = 3.
For n = 4, we have z[0] = 1, z[1] = 3, z[2] = 3, z[3] = 2, z[4] = 6, and z[5] = 0, so a(4) = 5.
For n = 5, we have z[0] = 1, z[1] = 3, z[2] = 2, z[3] = 6, and z[4] = 0, so a(5) = 4.

Mathematica

For[n=1, n<50, n++, k=0; Clear[z]; z[0]=1; z[k_]:=z[k]=Mod[3z[k-1], k+n];
While[z[k]>0, k++]; Print[k]; ] (* Petros Hadjicostas, Dec 14 2019, modification of a program in A177356 *)

Crossrefs

Cf. A177356, A208125.

Sequence in context: A250103 A063705 A184250 * A306977 A137655 A355621

Adjacent sequences: A330408 A330409 A330410 * A330412 A330413 A330414

Keyword

nonn

Author

Petros Hadjicostas, Dec 13 2019

Status

approved