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

Author

Jerry Metzger, Dec 10 2010

Keywords

• nonn
• easy

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.

Examples

			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]
		

Links

• 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.

Crossrefs

Cf. A208125, A330411.

Programs

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];]

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

Extensions

More terms from Petros Hadjicostas, Dec 13 2019