A127887 Indices of nonzero terms of A127886.

9, 18, 27, 28, 31, 33, 36, 37, 39, 41, 43, 47, 49, 50, 54, 55, 56, 57, 59, 62, 63, 65, 66, 71, 72, 73, 74, 78, 79, 82, 83, 86, 87, 89, 91, 94, 95, 97, 98, 99, 100, 103, 105, 107, 108, 109, 110, 111, 112, 114, 115, 118, 119, 121, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 135, 137, 139, 142, 143, 144, 145

Offset: 1

Author

David Applegate and N. J. A. Sloane, Feb 04 2007

Keywords

• nonn

Comments

These are the numbers for which allowing the choice of x/2 or 3x+1 in the "3x+1" iteration makes a difference in the minimal number of steps to reach 1.

Thus these are the n for which A006577(n) > A127885(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..695 (computed from the b-files of A006577 and A127885)

Crossrefs

Cf. A006577, A127885, A127886.

Programs

Mathematica

Position[#, k_ /; k > 0][[All, 1]] &@ Table[Length@ NestWhileList[If[OddQ@ #, 3 # + 1, #/2] &, n, # > 1 &] - Length@ NestWhileList[Flatten[# /. {k_ /; OddQ@ k :> 3 k + 1, k_ /; EvenQ@ k :> {k/2, 3 k + 1}}] &, {n}, FreeQ[#, 1] &], {n, 126}] (* Michael De Vlieger, Aug 20 2017 *)

Extensions

More terms from Antti Karttunen, Aug 18 2017