A352939 First differences of the records in the number of iterations of the 3x+1 sequences required to reach a power of 2.

3, 1, 8, 3, 1, 3, 88, 1, 3, 3, 3, 3, 3, 3, 13, 1, 26, 8, 3, 1, 26, 8, 21, 24, 6, 8, 3, 3, 26, 3, 13, 16, 11, 3, 21, 8, 3, 57, 6, 21, 39, 16, 3, 3, 26, 3, 3, 21, 13, 16, 52, 21, 3, 3, 13, 1, 39, 205, 1, 3, 3, 8, 1, 21, 1, 13, 8, 42, 37, 44, 1, 21, 31, 26, 3, 6, 1, 8, 6, 8, 13, 52, 1, 13, 3, 8, 3, 13, 8, 52, 3, 26, 3

Offset: 1

Author

Omar E. Pol, Apr 07 2022

Keywords

• nonn

Comments

First differences of the records in the number of nonpowers of 2 in the sequences 3x+1.

Is this a finite sequence?

Closely related to A288493 (perhaps the same after initial terms). - R. J. Mathar, May 20 2022

Examples

			The first 10 terms of A208981 are 0, 0, 3, 0, 1, 4, 12, 0, 15, 2. The records are 0, 3, 4, 12, 15. The first differences of these records are 3, 1, 8, 3, the same as the first four terms of this sequence.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..146 (b-file generated using Eric Roosendaal's data and _Omar E. Pol_'s comment in A006877).
• Eric Roosendaal, 3x+1 Delay Records
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

First differences of A352907.

Cf. A347270 (gives all 3x+1 sequences).

Cf. A006370, A006877, A014682, A056959, A057716, A208981, A347272, A347519, A347532, A353265.

Programs

Mathematica

f[n_] := -1 + Length @ NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, ! IntegerQ @ Log[2, #] &]; Differences @ Union @ FoldList[Max, Array[f, 10^5]] (* Amiram Eldar, Apr 08 2022 *)

Extensions

More terms from Paolo Xausa, Jun 22 2022