

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.


2



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
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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[k1] 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[k1] mod (k + n)) for k = 1..m}.  Petros Hadjicostas, Dec 13 2019


EXAMPLE

For n = 15, the zsequence 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[k1], k+n];
While[z[k]>0, k++]; Print[k]; ]


CROSSREFS

Cf. A208125, A330411.
Sequence in context: A099796 A022831 A064365 * A078322 A252867 A194356
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



