Geodesic
Complementary equations
Journal of integer sequences, Tome 10 (2007) no. 1
Zbl   EuDML
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 
Kimberling,  Clark. Complementary equations. Journal of integer sequences, Tome 10 (2007) no. 1. http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a1/
@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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