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A352939
First differences of the records in the number of iterations of the 3x+1 sequences required to reach a power of 2.
3
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
1,1
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
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
EXAMPLE
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.
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 *)
CROSSREFS
First differences of A352907.
Cf. A347270 (gives all 3x+1 sequences).
Sequence in context: A185452 A179449 A049541 * A249757 A207609 A322428
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 07 2022
EXTENSIONS
More terms from Paolo Xausa, Jun 22 2022
STATUS
approved