%I #34 Jan 14 2024 02:32:06

%S 7,9,11,13,23,25,27,61,71,73,75,77,87,89,91,125,135,137,139,141,151,

%T 153,155,189,199,201,203,205,215,217,219,253,263,265,267,269,279,281,

%U 283,317,327,329,331,333,343,345,347,381,391,393,395,397,407,409,411,445

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

%C Initially, first differences are 8-periodic: 2,2,2,10,2,2,34,10. [Unsigned comment made accurate by _Peter Munn_, Jan 13 2024]

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

%F Conjectures from _Chai Wah Wu_, Feb 01 2018: (Start)

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

%F 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)

%F The above conjectures are incompatible with A102370(2^37-37) = 2^38-3. - _Peter Munn_, Jan 13 2024

%t 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 *)

%Y Cf. A102370.

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

%K nonn,base

%O 1,1

%A _Philippe Deléham_, Mar 31 2005

%E More terms from _Robert G. Wilson v_, Mar 30 2005