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%I #41 Jul 13 2022 07:23:04
%S 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,
%T 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,
%U 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
%N First differences of the records in the number of iterations of the 3x+1 sequences required to reach a power of 2.
%C First differences of the records in the number of nonpowers of 2 in the sequences 3x+1.
%C Is this a finite sequence?
%C Closely related to A288493 (perhaps the same after initial terms). - _R. J. Mathar_, May 20 2022
%H Paolo Xausa, <a href="/A352939/b352939.txt">Table of n, a(n) for n = 1..146</a> (b-file generated using Eric Roosendaal's data and _Omar E. Pol_'s comment in A006877).
%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/delrecs.html">3x+1 Delay Records</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 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.
%t 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 *)
%Y First differences of A352907.
%Y Cf. A347270 (gives all 3x+1 sequences).
%Y Cf. A006370, A006877, A014682, A056959, A057716, A208981, A347272, A347519, A347532, A353265.
%K nonn
%O 1,1
%A _Omar E. Pol_, Apr 07 2022
%E More terms from _Paolo Xausa_, Jun 22 2022