A347532 -id:A347532 - cp's OEIS frontend

A352907 Records in the number of iterations in the 3x+1 sequences required to reach a power of 2.

0, 3, 4, 12, 15, 16, 19, 107, 108, 111, 114, 117, 120, 123, 126, 139, 140, 166, 174, 177, 178, 204, 212, 233, 257, 263, 271, 274, 277, 303, 306, 319, 335, 346, 349, 370, 378, 381, 438, 444, 465, 504, 520, 523, 526, 552, 555, 558, 579, 592, 608, 660, 681, 684

Offset: 1

Omar E. Pol, Apr 07 2022

nonn

Records of the number of nonpowers of 2 in the sequences 3x+1.

Is this a finite sequence?

Paolo Xausa, Table of n, a(n) for n = 1..147 (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

Records in A208981.
Cf. A352939 (first differences).
Cf. A347270 (gives all 3x+1 sequences).
Cf. A006370, A006877, A014682, A056959, A057716, A347272, A347519, A347532, A353265.

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

More terms from Alois P. Heinz, Apr 07 2022

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

Original entry on oeis.org

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

Omar E. Pol, Apr 07 2022

nonn

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

			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.

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

First differences of A352907.
Cf. A347270 (gives all 3x+1 sequences).
Cf. A006370, A006877, A014682, A056959, A057716, A208981, A347272, A347519, A347532, A353265.

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 *)

More terms from Paolo Xausa, Jun 22 2022

cp's OEIS Frontend

A352907 Records in the number of iterations in the 3x+1 sequences required to reach a power of 2.

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