A338719 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = ceiling(b(n)).

1, 2, 2, 3, 2, 4, 3, 4, 3, 5, 3, 5, 3, 5, 4, 6, 4, 6, 4, 6, 4, 6, 4, 7, 5, 7, 5, 7, 5, 7, 5, 8, 5, 8, 5, 8, 5, 8, 6, 8, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 10, 6, 10, 6, 10, 7, 10, 7, 10, 7, 10, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

R:= 1:
b:= 1:
for i from 2 to 100 do
  b:= i/b;
  R:= R, ceil(b)
od:
R; # Robert Israel, Jul 21 2024

Crossrefs

Cf. A338718, A338720.

For the numerators and denominators of b(n) see A004731 and A004730.

Sequence in context: A339147 A062821 A353862 * A296080 A180633 A286610

Adjacent sequences: A338716 A338717 A338718 * A338720 A338721 A338722

Keyword

nonn,look

Author

N. J. A. Sloane, Nov 29 2020, following a suggestion from Anchar Koops, Nov 24 2020

Status

approved