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A338720
Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = nearest integer to b(n).
3
1, 2, 2, 3, 2, 3, 2, 4, 2, 4, 3, 4, 3, 5, 3, 5, 3, 5, 4, 6, 4, 6, 4, 6, 4, 6, 4, 7, 4, 7, 4, 7, 5, 7, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 9, 5, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 7, 10, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 12, 7, 12, 7
OFFSET
1,2
COMMENTS
Since b(3) = 3/2, a(3) could also be taken to be 1.
EXAMPLE
The first few fractions b(n) are 1, 2, 3/2, 8/3, 15/8, 16/5, 35/16, 128/35, 315/128, 256/63, 693/256, 1024/231, 3003/1024, 2048/429, ...
MAPLE
A338720b := proc(n)
option remember ;
if n = 1 then
1;
else
n/procname(n-1) ;
end if;
end proc:
A338720 := proc(n)
round(A338720b(n)) ;
end proc:
seq(A338720(n), n=1..87) ; # R. J. Mathar, Dec 01 2020
MATHEMATICA
b[n_] := b[n] = If[n == 1, 1, n/b[n-1]];
a[n_] := Round[b[n]];
Table[a[n], {n, 1, 87}] (* Jean-François Alcover, Apr 23 2023 *)
CROSSREFS
For the numerators and denominators of b(n) see A004731 and A004730.
Sequence in context: A052180 A065151 A345874 * A320013 A299990 A175193
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 29 2020, following a suggestion from Anchar Koops, Nov 24 2020
STATUS
approved