OFFSET
1,1
COMMENTS
For a given integer m, write its binary representation in reverse order, as in A125626, A125754, etc.; let a 0 mean "halving" and a 1 mean "k -> 3k+1". Then m specifies an operation on real numbers given by k -> f_m(k). Suppose the equation f_m(k) = k has a positive integer solution for some m. Then we conjecture that the values of k are precisely the terms of this sequence.
25 is a term because we have 25 -> 76 -> 38 -> 19 -> 58 -> 29 -> 88 -> 44 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 25.
In other words, we conjecture that this sequence coincides with A125757 sorted and with duplicates removed.
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
From R. J. Mathar, Apr 03 2009: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 9.
a(n) + a(n+1) = A017185(n).
G.f.: x*(4+3*x+2*x^2)/((1+x)*(x-1)^2). (End)
E.g.f.: 2 + ((9*x - 5/2)*exp(x) - (3/2)*exp(-x))/2. - David Lovler, Aug 21 2022
MATHEMATICA
Select[Range[300], MemberQ[{4, 7}, Mod[#, 9]]&] (* Harvey P. Dale, Mar 12 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and David Applegate, Feb 02 2007
STATUS
approved