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A177356 a(n) = index of first 0 term in rumor sequence with initial term 1 and parameters b=2 and n 0
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 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

B. Dearden, J. Iiams, J. Metzger, Rumor Arrays, Journal of Integer Sequences, 16 (2013), #13.9.3.

LINKS

Table of n, a(n) for n=1..47.

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

EXAMPLE

Example: For n = 15, the z-sequence terms are 1,2,4,8,16,12,3,6,12,0, so a[15] = 9.

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

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

STATUS

approved

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Last modified August 28 18:07 EDT 2015. Contains 261154 sequences.