

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

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



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


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



KEYWORD

nonn


AUTHOR



STATUS

approved



