OFFSET
1
COMMENTS
Write a(n) = [(b*n+c)*r] - b*[n*r] - [c*r]. If r>0 and b and c are integers satisfying b >= 2 and 0 <= c <= b-1, then 0 <= a(n) <= b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = floor(2*n*sqrt(3)) - 2*floor(n*sqrt(3)).
MATHEMATICA
PROG
(PARI) for(n=1, 100, print1(floor(2*n*sqrt(3)) - 2*floor(n*sqrt(3)), ", ")) \\ G. C. Greubel, Apr 20 2018
(Magma) [Floor(2*n*Sqrt(3)) - 2*Floor(n*Sqrt(3)): n in [1..100]]; // G. C. Greubel, Apr 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 16 2011
STATUS
approved