

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



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
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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



