A222755 Greatest odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.

1, 0, 0, 5, 0, 21, 17, 85, 113, 341, 453, 1365, 1813, 5461, 7281, 21845, 29125, 87381, 116501, 349525, 466033, 1398101, 1864133, 5592405, 7456533, 22369621, 29826161, 89478485, 119304645, 357913941, 477218581, 1431655765

Offset: 0

Author

T. D. Noe, Mar 04 2013

Keywords

• nonn

Comments

Note that a(n) <= 2^n, with equality only for n = 0.

Crossrefs

Cf. A222752, A222753, A222754.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]] = n], {n, 1, 2^(nn - 1), 2}]; t

Extensions

a(31) added - T. D. Noe, Mar 05 2013