A386819 Indices of records in A389240.

1, 2, 3, 5, 10, 13, 26, 52, 61, 122, 244, 381, 762, 1021, 2042, 4084, 8168, 16336, 32672, 65344, 130688, 261376, 522752, 1045504, 2091008, 3145725, 6291450, 12582900, 25165800, 50331600, 100663200, 201326400, 268435453, 536870906, 1073741812

Offset

1,2

Comments

A389240(n) is the number of steps to reach 1 when the sequence S starts with S(1) = n and is extended with S(m)/2 when S(m) is even, otherwise with S(m) + the smallest odd number not yet added.

Links

Table of n, a(n) for n=1..35.

Example

Let s = A389240.
Table of n, a(n), and s(a(n)) for n <= 12:
 n   a(n) s(a(n))
--------------
 1     1     0
 2     2     1
 3     3     3
 4     5     8
 5    10     9
 6    13    33
 7    26    34
 8    52    35
 9    61    96
10   122    97
11   244    98
12   381   120

Mathematica

Lim=200000; s=Table[m = -1; If[#[[-1]] == 1, -1 + Length[#], -1] &@ If[n < 5, NestWhileList[If[EvenQ[#], #/2, # + (m += 2)] &, n, # > 1 &],  NestWhileList[If[EvenQ[#], #/2, # + (m += 2)] &, n, And[#4 > 1, Nand[#1 == #3 - 2, #2 == #4 - 4]] &, 4]], {n, Lim}]; rec={0}; Ind={1}; Do[If[s[[n]]>rec[[-1]], AppendTo[rec, s[[n]]]; AppendTo[Ind, n]], {n, Lim}]; Ind

Crossrefs

Cf. A389240, A389391.

Sequence in context: A103746 A071848 A268176 * A120938 A120610 A090859

Adjacent sequences: A386816 A386817 A386818 * A386820 A386821 A386822

Keyword

nonn,more

Author

James C. McMahon, Oct 07 2025

Extensions

a(31)-a(35) from Sean A. Irvine, Oct 15 2025

Status

approved