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

Author

Michael De Vlieger, Aug 26 2017

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A006577, A127885, A127886, A290100.

Programs

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}]