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A330411
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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"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]
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LINKS
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B. Dearden, J. Iiams, and J. Metzger, Rumor Arrays, J. Integer Seq. 16 (2013), #13.9.3.
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FORMULA
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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}.
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EXAMPLE
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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.
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MATHEMATICA
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For[n=1, n<50, n++, k=0; Clear[z]; z[0]=1; z[k_]:=z[k]=Mod[3z[k-1], k+n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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