OFFSET
1,1
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.
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
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Philippe Deléham, Mar 31 2005
EXTENSIONS
More terms from Robert G. Wilson v, Mar 30 2005
STATUS
approved