A352939 -id:A352939 - 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

A353265 Partial sums of A208981.

Original entry on oeis.org

0, 0, 3, 3, 4, 8, 20, 20, 35, 37, 47, 52, 57, 70, 83, 83, 91, 107, 123, 126, 127, 138, 149, 155, 174, 180, 287, 301, 315, 329, 431, 431, 453, 462, 471, 488, 505, 522, 552, 556, 661, 663, 688, 700, 712, 724, 824, 831, 851, 871, 891, 898, 905, 1013, 1121, 1136, 1164, 1179, 1207, 1222, 1237, 1340, 1443, 1443

Offset: 1

Omar E. Pol, Apr 09 2022

nonn

Cf. A208981, A347270 (gives all 3x+1 sequences).

Cf. A006370, A006877, A014682, A347272, A347519, A352907, A352908, A352939.

Accumulate @ Table[-1 + Length @ NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, ! IntegerQ @ Log[2, #] &], {n, 1, 64}] (* Amiram Eldar, Apr 09 2022 *)

ispow2(n)=n>>=valuation(n, 2); n==1;
f(n) = my(s); while(!ispow2(n), n=if(n%2, 3*n+1, n/2); s++); s; \\ A208981
a(n) = sum(i=1, n, f(i)); \\ Michel Marcus, Apr 13 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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