|
|
A022330
|
|
Index of 3^n within sequence of numbers of form 2^i*3^j (A003586).
|
|
9
|
|
|
1, 3, 7, 12, 19, 27, 37, 49, 62, 77, 93, 111, 131, 152, 175, 199, 225, 252, 281, 312, 344, 378, 413, 450, 489, 529, 571, 614, 659, 705, 753, 803, 854, 907, 961, 1017, 1075, 1134, 1195, 1257, 1321, 1386, 1453, 1522, 1592, 1664, 1737, 1812, 1889, 1967, 2047, 2128
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(1000)=793775, a(10000)=79261054, a(100000)=7924941755, a(1000000)=792482542841.
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ kn^2 with k = log(3)/log(4) = 0.792.... More exact asymptotics? - Zak Seidov, Dec 22 2011
kn^2 + kn + 1 <= a(n) <= kn^2 + (k+1)n + 1, so a(n) = kn^2 + O(n) with k = log(3)/log(4). The law of the iterated logarithm suggests that a better error term might be possible. - Charles R Greathouse IV, Nov 28 2022
|
|
MATHEMATICA
|
c[0] = 1; c[n_] := 1 + Sum[Ceiling[j*Log[2, 3]], {j, n}]; Table[c[i], {i, 0, 51}] (* Norman Carey, Jun 13 2012 *)
|
|
PROG
|
(PARI) listsm(lim)=my(v=List(), N); for(n=0, log(lim)\log(3), N=3^n; while(N<=lim, listput(v, N); N<<=1)); v=Vec(v); vecsort(v)
list(lim)=my(v=listsm(3^floor(lim))); vector(floor(lim+1), i, setsearch(v, 3^(i-1))) \\ Charles R Greathouse IV, Aug 19 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|