OFFSET
1,1
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((3*n+1)*(1+sqrt(5))/2) - 3*floor(n*(1+sqrt(5))/2) - 1. - G. C. Greubel, Apr 06 2018
MATHEMATICA
PROG
(PARI) for(n=1, 100, print1(floor((3*n+1)*(1+sqrt(5))/2) - 3*floor(n*(1+sqrt(5))/2) - 1, ", ")) \\ G. C. Greubel, Apr 06 2018
(Magma) [Floor((3*n+1)*(1+Sqrt(5))/2) - 3*Floor(n*(1+Sqrt(5))/2) - 1: n in [1..100]]; // G. C. Greubel, Apr 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 10 2011
STATUS
approved