Geodesic
Complementary equations
Journal of integer sequences, Tome 10 (2007) no. 1
Increasing sequences $a$( ) and $b$( ) that partition the sequence of positive integers are called complementary sequences, and equations that explicitly involve both $a$( ) and $b$( ) are called complementary equations. This article surveys several families of such equations, including $b(n) = a(jn) +- r, b(n) = a(jn)+kn, b(n) = f(a(n))$, and $b(n) = a(b(n-1))+qn+r$.
Classification : 11B37
Keywords: Beatty sequence, complementary equation, complementary sequences, dispersion, inverse, polygonal numbers, stolarsky array, wythoff array, wythoff difference array, wythoff sequences 
@article{JIS_2007__10_1_a1,
     author = {Kimberling,  Clark},
     title = {Complementary equations},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {1},
     zbl = {1117.11014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a1/}
}
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Kimberling,  Clark. Complementary equations. Journal of integer sequences, Tome 10 (2007) no. 1. http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a1/