|
| |
|
|
A007067
|
|
Nearest integer to n*tau.
(Formerly M0622)
|
|
57
|
|
|
|
0, 2, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 74, 76, 78, 79, 81, 83, 84, 86, 87, 89, 91, 92, 94, 95, 97, 99, 100, 102, 104, 105
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
First column of inverse Stolarsky array.
A rectangle of size a(n) X n approximates a golden rectangle. So does A295282(n) X n, which targets the golden ratio's underlying objective. These approximations differ first for n = 4 and generally if n = F(6*k)/2, where F(n) = A000045(n) is the n-th Fibonacci number and k >= 1. - Peter Munn, Jan 12 2018
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
Iain Fox, Table of n, a(n) for n = 0..10000 (first 1001 terms from Vincenzo Librandi)
Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, Classic Sequences
|
|
|
FORMULA
|
Satisfies a(a(n)) = a(n) + n. - Franklin T. Adams-Watters, Aug 14 2006
a(n) = floor((A066096(2*n) + 1)/2). - Peter Munn, Jan 12 2018
|
|
|
MAPLE
|
A007067:=n->round(n*(1+sqrt(5))/2); seq(A007067(n), n=0..100); # Wesley Ivan Hurt, Nov 27 2013
|
|
|
MATHEMATICA
|
a[n_] := Round[n*GoldenRatio]; Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jun 27 2012 *)
|
|
|
PROG
|
(PARI) a(n) = round(n*(1+sqrt(5))/2) \\ Michel Marcus, May 20 2013
(Python)
from math import isqrt
def A007067(n): return (isqrt(5*n**2<<2)>>1)+n+1>>1 # Chai Wah Wu, Aug 26 2022
|
|
|
CROSSREFS
|
Cf. A166946 (characteristic function), A007064 (complement).
Different from A026355.
Sequences with similar terms: A022342, A295282.
Other roundings of n*tau: A000201, A004956, A066096.
Cf. A000045 (Fibonacci numbers), A001622 (value of tau).
Sequence in context: A029921 A026355 A099267 * A186322 A092979 A135260
Adjacent sequences: A007064 A007065 A007066 * A007068 A007069 A007070
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Mira Bernstein
|
|
|
STATUS
|
approved
|
| |
|
|
