A172128 -id:A172128 - cp's OEIS frontend

A181885 Integer nearest (1/n)*(r^n), where r = golden ratio = (1 + sqrt(5))/2.

2, 1, 1, 2, 2, 3, 4, 6, 8, 12, 18, 27, 40, 60, 91, 138, 210, 321, 492, 756, 1166, 1800, 2786, 4320, 6710, 10440, 16267, 25380, 39650, 62017, 97108, 152214, 238824, 375060, 589521, 927369, 1459960, 2300100

Offset: 1

Clark Kimberling, Nov 20 2010

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000045, A172128.

[Round(((1 + Sqrt(5))/2)^n/n): n in [1..50]]; // Vincenzo Librandi, Jun 21 2011

Table[Round[((1 + Sqrt[5])/2)^n/n], {n, 1, 50}]

a(n) = floor(1/2 + (1/n)*(r^n)), where r = golden ratio = (1 + sqrt(5))/2.

A242926 a(n) = denominator of B(0,n), where B(n,n) = 0, B(n-1,n) = 1/n and otherwise B(m,n) = B(m-1,n+1) - B(m-1,n).

Original entry on oeis.org

1, 1, 1, 2, 1, 6, 1, 4, 3, 5, 1, 4, 1, 7, 15, 8, 1, 18, 1, 10, 21, 11, 1, 24, 5, 13, 9, 14, 1, 30, 1, 16, 11, 17, 35, 12, 1, 19, 39, 20, 1, 42, 1, 22, 9, 23, 1, 48, 7, 25, 17, 26, 1, 54, 55, 28, 19, 29, 1, 20, 1

Offset: 0

Paul Curtz, May 26 2014

nonn

The numerators are A189731(n).
B(0,n) = 0, 1, 1, 3/2, 2, 17/6, 4, 23/4, 25/3, 61/5, 18, 107/4, 40, 421/7, ...
is a super autosequence as defined in A242563.
The positive integers in B(0,n) give A064723(n). Corresponding rank: A006093(n+1). B(0,n) is linked to the primes A000040.
Divisor of B(0,n), n > 0: 1, 1, 1, 2, 2, 4, 5, ... = A172128(n+1).
Common (LCM) denominators for the antidiagonals: 1, 1, 1, 2, 2, 6, 6, 12, 12, ... = A139550(n+1)?.
1 = 1
1/2 +  3/2 = 2
1/3 +  5/6 + 17/6 = 4
1/4 + 7/12 +  7/4 + 23/4 = 25/3
etc.
The positive terms of the first bisection are the sum of the corresponding antidiagonal terms upon the 0's.
0 followed by A001610(n), i.e., 0, 0, 2, 3, 6, 10, 17, ... is an autosequence of the second kind.

Cf. A000204, A175386, A001610, A189731, A139550, A242563.

Table[Denominator[(LucasL[n+1]-1)/(n+1)], {n, 0, 100}] (* Artur Jasinski, Nov 06 2022 *)

a(2n+1) = A175386(n).
a(n) = denominator(A001610(n)/(n+1)). [edited by Michel Marcus, Nov 14 2022]
a(n) = denominator((A000204(n+1) - 1)/(n+1)). - Artur Jasinski, Nov 06 2022

a(24)-a(60) from Jean-François Alcover, May 26 2014

cp's OEIS Frontend

A181885 Integer nearest (1/n)*(r^n), where r = golden ratio = (1 + sqrt(5))/2.

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