A291213 Start from the singleton set S = {n}, and unless 1 is already a member of S, generate on each iteration a new set where each odd number k is replaced by 3k+1, and each even number k is replaced by 3k+1 and k/2. a(n) is the total size of the set from the singleton through after the first iteration which has produced 1 as a member, inclusive.

1, 3, 36, 6, 20, 72, 1168, 11, 216, 35, 576, 143, 111, 2422, 1657, 19, 336, 378, 6253, 66, 51, 1167, 820, 241, 24096, 180, 18805, 215, 3833, 3488, 368905, 31, 3460, 575, 426, 716, 576, 12387, 57556, 110, 10513, 83, 8948, 2303, 1782, 1656, 175195, 387, 1647

Offset

1,2

Comments

See comments at A290100.

A290100(n) is the size of the set at the last iteration, while this sequence is the sum of sizes of all generations including the last iteration.

A290100(n)/A291213(n) < 29/90 for n = {6, 67, 81, 92, 102, 153, 155, 165, 198, 201, 202, 204, 205, 217, 228, 235, 264, 265, 289, 299, 308, 309, 349, 353, 360, 396, 408, 434, ...}, with n = 6 the greatest observed difference. - Michael De Vlieger, Aug 30 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..450

Example

For n = 5:
Generation   Set
1 (1 term)   5
2 (1 term)   16
3 (2 terms)  8, 49
4 (3 terms)  4, 25, 148
5 (5 terms)  2, 13, 74, 76, 445
6 (8 terms)  1, 7, 37, 38, 40, 223, 229, 1336
thus a(5) = 20 and A290100(5) = 8.

Mathematica

Table[Length@ Flatten@ NestWhileList[Union@ Flatten[# /. {k_ /; OddQ@ k :> 3 k + 1, k_ /; EvenQ@ k :> {k/2, 3 k + 1}}] &, {n}, FreeQ[#, 1] &], {n, 49}]

Crossrefs

Cf. A006577, A127885, A127886, A290100.

Sequence in context: A119526 A112404 A189216 * A158301 A105758 A214852

Adjacent sequences: A291210 A291211 A291212 * A291214 A291215 A291216

Keyword

nonn

Author

Michael De Vlieger, Aug 26 2017

Status

approved