A123247 Let S(1)={1} and, for n>1 let S(n) be the smallest set containing x, x+1, 2x and 3x for each element x in S(n-1). a(n) is the number of elements in S(n).

1, 3, 6, 13, 27, 54, 107, 213, 423, 845, 1685, 3371, 6735, 13468, 26937, 53900, 107873, 216035, 432787, 867313, 1738728, 3486464, 6993111, 14029776, 28153533, 56507114, 113435141, 227755613, 457358671, 918562597

Offset

1,2

Comments

If the set mapping has x -> x, 2x, 3x, 5x is used instead of x -> x, x+1, 2x, 3x, the corresponding sequence consists of the tetrahedral numbers C(n+3,3) = A000292.

Links

Table of n, a(n) for n=1..30.

Example

Under the indicated set mapping we have {1} -> {1,2,3} -> {1,2,3,4,6,9} -> {1,2,3,4,5,6,7,8,9,10,12,18,27}, ..., so a(2)=3, a(3)=6, a(4)=13, etc.

Prog

(PARI) lista(nn) = {my(k, v=[1]); print1(1); for(n=2, nn, v=Set(vector(4*#v, i, if(k=i%4, k*v[(3+i)\4], v[i/4]+1))); print1(", ", #v)); } \\ Jinyuan Wang, Apr 14 2020
(Python)
from itertools import chain, islice
def A123247_gen(): # generator of terms
    s = {1}
    while True:
        yield len(s)
        s = set(chain.from_iterable((x, x+1, 2*x, 3*x) for x in s))
A123247_list = list(islice(A123247_gen(), 20)) # Chai Wah Wu, Jan 12 2022

Crossrefs

Cf. A000292, A122554, A168043.

Sequence in context: A281638 A281100 A276129 * A212444 A112306 A291753

Adjacent sequences: A123244 A123245 A123246 * A123248 A123249 A123250

Keyword

nonn,more

Author

John W. Layman, Oct 04 2006

Extensions

a(14)-a(25) from Jinyuan Wang, Apr 14 2020

a(26)-a(30) from Chai Wah Wu, Jan 12 2022

Status

approved