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

Author

John W. Layman, Oct 04 2006

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

Cf. A000292, A122554, A168043.

Programs

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

Extensions

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

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