A123247 - OEIS

%I #18 Mar 21 2023 15:23:25

%S 1,3,6,13,27,54,107,213,423,845,1685,3371,6735,13468,26937,53900,

%T 107873,216035,432787,867313,1738728,3486464,6993111,14029776,

%U 28153533,56507114,113435141,227755613,457358671,918562597

%N 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).

%C 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.

%e 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.

%o (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

%o (Python)

%o from itertools import chain, islice

%o def A123247_gen(): # generator of terms

%o     s = {1}

%o     while True:

%o         yield len(s)

%o         s = set(chain.from_iterable((x,x+1,2*x,3*x) for x in s))

%o A123247_list = list(islice(A123247_gen(),20)) # _Chai Wah Wu_, Jan 12 2022

%Y Cf. A000292, A122554, A168043.

%K nonn,more

%O 1,2

%A _John W. Layman_, Oct 04 2006

%E a(14)-a(25) from _Jinyuan Wang_, Apr 14 2020

%E a(26)-a(30) from _Chai Wah Wu_, Jan 12 2022