A103621 Trajectory of 7 under repeated application of the map n -> A102370(n).

7, 9, 11, 13, 23, 25, 27, 61, 71, 73, 75, 77, 87, 89, 91, 125, 135, 137, 139, 141, 151, 153, 155, 189, 199, 201, 203, 205, 215, 217, 219, 253, 263, 265, 267, 269, 279, 281, 283, 317, 327, 329, 331, 333, 343, 345, 347, 381, 391, 393, 395, 397, 407, 409, 411, 445

Offset: 1

Author

Philippe Deléham, Mar 31 2005

Keywords

• nonn
• base

Comments

Initially, first differences are 8-periodic: 2,2,2,10,2,2,34,10. [Unsigned comment made accurate by Peter Munn, Jan 13 2024]

Links

• 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.

Crossrefs

Cf. A102370.

Trajectories of other numbers A103192 (1), A103747 (2), A158953 (12), A159887 (29).

Programs

Mathematica

f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[ Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s + n]; NestList[f, 7, 55] (* Robert G. Wilson v, Mar 30 2005 *)

Formula

Conjectures from Chai Wah Wu, Feb 01 2018: (Start)

a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.

G.f.: x*(3*x^8 + 34*x^7 + 2*x^6 + 2*x^5 + 10*x^4 + 2*x^3 + 2*x^2 + 2*x + 7)/(x^9 - x^8 - x + 1). (End)

The above conjectures are incompatible with A102370(2^37-37) = 2^38-3. - Peter Munn, Jan 13 2024

Extensions

More terms from Robert G. Wilson v, Mar 30 2005