OFFSET
1,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n + A214990(n).
EXAMPLE
Let r = (3+sqrt(5))/2 = 1 + golden ratio,
n . . n*r . . nearest integer . second nearest
1 . . 2.618... . 3 . . . . . . . 2 = a(1)
2 . . 5.236... . 5 . . . . . . . 6 = a(2)
3 . . 7.854... . 8 . . . . . . . 7 = a(3)
4 . . 10.472.. . 10. . . . . . . 11 = a(4)
5 . . 13.090.. . 13. . . . . . . 14 = a(5)
MATHEMATICA
r = GoldenRatio^2; f[x_] := If[FractionalPart[x] < 1/2, Ceiling[x], Floor[x]]
Table[f[r*n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Oct 31 2012
STATUS
approved