A112420 Leading digits in 3x+1 chain starting with the number 1117065.

1, 3, 1, 8, 2, 1, 3, 1, 5, 2, 1, 4, 2, 6, 3, 1, 4, 2, 7, 3, 1, 5, 1, 8, 4, 1, 6, 1, 9, 2, 1, 4, 2, 6, 3, 9, 4, 1, 6, 3, 1, 5, 1, 7, 2, 1, 3, 1, 5, 2, 7, 3, 1, 5, 1, 8, 4, 1, 6, 1, 9, 2, 1, 7, 3, 1, 9, 4, 2, 6, 3, 1, 5, 2, 1, 3, 1, 5, 2, 8, 4, 1, 6, 1, 9, 2, 1, 4, 2, 6, 3, 1, 8, 2, 1, 3, 1, 5, 2, 1, 4, 2, 6, 3, 1

Offset: 1

Author

Lekraj Beedassy, Dec 10 2005

Keywords

• nonn
• base

Comments

The 3x+1 chain starts 1117065 -> 3351196 -> 1675598 -> 837799 and enters a 4->2->1->4->.. cycle after 527 iterations. The current sequence shows the most significant decimal digit after each iteration. [R. J. Mathar, Jul 26 2010]

Links

• Michel Marcus, Table of n, a(n) for n = 1..600
• A. V. Kontorovich & S. J. Miller, Benford's Law, Values Of L-Functions And The 3x+1 Problem, arXiv:math/0412003 [math.NT], 2004-2005.
• J. C. Lagarias and K. Soundararajan, Benford's Law for the 3x+1 Function, arXiv:math/0509175 [math.NT], 2005-2006.
• P. Picart, Algorithme de Collatz et conjecture de Syracuse
• Index entries for sequences related to Benford's law

Crossrefs

Cf. A033958.

Programs

PARI

lista(nn) = my(c = 1117065); for (n=1, nn, print1(digits(c)[1], ", "); if (c % 2, c = 3*c+1, c = c/2);); \\ Michel Marcus, Nov 05 2016

Extensions

a(103) corrected by Michel Marcus, Nov 05 2016