A177356 a(n) is the index of the first 0 term in the rumor sequence with initial 0th term 1 and parameters b = 2 and n.

1, 2, 5, 10, 3, 18, 7, 24, 23, 22, 13, 4, 19, 18, 9, 6, 15, 374, 13, 12, 11, 370, 369, 32, 367, 366, 5, 28, 363, 8, 361, 360, 37, 358, 21, 356, 355, 354, 353, 16, 351, 100, 349, 98, 347, 346, 95, 344, 93, 92, 91, 340, 89, 10, 15, 336, 31, 6, 333, 82, 331, 80, 25, 328, 327, 326

Offset

1,2

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.

Links

Table of n, a(n) for n=1..66.

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] = (2*z[k-1] mod (k + n)) for k = 1..m}. - Petros Hadjicostas, Dec 13 2019

Example

For n = 15, the z-sequence terms are 1, 2, 4, 8, 16, 12, 3, 6, 12, 0, so a(15) = 9; that is, z[0] = 1, z[1] = 2, z[2] = 4, ..., z[8] = 12, and z[9] = 0. [Edited by Petros Hadjicostas, Dec 13 2019]

Mathematica

For[n=1, n<50, n++, k=0; Clear[z]; z[0]=1; z[k_]:=z[k]=Mod[2z[k-1], k+n];
While[z[k]>0, k++]; Print[k]; ]

Crossrefs

Cf. A208125, A330411.

Sequence in context: A099796 A022831 A064365 * A078322 A252867 A352199

Adjacent sequences: A177353 A177354 A177355 * A177357 A177358 A177359

Keyword

nonn,easy

Author

Jerry Metzger, Dec 10 2010

Extensions

More terms from Petros Hadjicostas, Dec 13 2019

Status

approved