A338720 -id:A338720 - cp's OEIS frontend

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

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

			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, ...

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

Cf. A338718, A338720.

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

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

A338718 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = floor(b(n)).

Original entry on oeis.org

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

Offset: 1

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

nonn

			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, ...

Cf. A338719, A338720.

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

a[n_] := Floor[n!!/(n - 1)!!]; Array[a, 90] (* Robert G. Wilson v, Dec 06 2020 *)

cp's OEIS Frontend

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

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