A103747 Trajectory of 2 under repeated application of the map n -> A102370(n).

2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290, 294, 298, 302, 306, 310, 314, 382, 386, 390, 394, 398, 402, 406, 410, 414, 418, 422

Offset: 1

Author

Benoit Cloitre and David Applegate, Mar 25 2005

Keywords

• nonn
• base

Comments

Although it initially appears that a(n)-8n is the 16-periodic sequence {-2,-6,-10,-14,-18,-22,-26,-30,-34,-38,-42,-46,-50,-54,6,2}, this pattern eventually breaks down. However, the first divergence occurs beyond the first 400 million terms.

(a(n)) agrees with the 16-periodic sequence up to a(2^67-1) = 2^70 - 70, but then diverges with a(2^67) = 2^71 - 2. - Charlie Neder, Feb 07 2019

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps], preprint, 2005.
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
• Index entries for sequences which agree for a long time but are different

Crossrefs

Cf. A102370, A132417.

Trajectories of other numbers: A103192 (1), A103621 (7), A158953 (12), A159887 (29).

Programs

Haskell

a103747 n = a103747_list !! (n-1)
a103747_list = iterate (fromInteger . a102370) 2
-- Reinhard Zumkeller, Jul 21 2012

Extensions

Edited by Peter Munn, Jan 13 2024