1,1

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.

In other words, we conjecture that this sequence coincides with A125757 sorted and with duplicates removed.

a(n)=[11-3*(-1)^n]/2 + 9*A004526 - Paolo P. Lava (ppl(AT)spl.at), Nov 05 2007

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). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 03 2009]

a(n)=9*n-a(n-1)-7 (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 25 2009]

25 is a member 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.

For n=2, a(2)=9*2-4-7=7; n=3, a(3)=9*3-7-7=13; n=4, a(4)=9*4-13-7=16 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 25 2009]

Cf. A125626, A125754, A125755, A125756, A125757, A125710, A125711.

Sequence in context: A045090 A031149 A074273 this_sequence A151788 A048297 A061201

Adjacent sequences: A125755 A125756 A125757 this_sequence A125759 A125760 A125761

nonn

N. J. A. Sloane (njas(AT)research.att.com) and David Applegate (david(AT)research.att.com), Feb 02 2007