Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 235.10006
Autor: Erdös, Paul; Graham, Ronald L.
Title: On sums of Fibonacci numbers. (In English)
Source: Fibonacci Q. 10, 249-254 (1972).
Review: A sequence of integers 1 \leq a1 \leq a2 \leq ... is called complete if every sufficiently large integer n can be written in the form (1) n = sum \epsiloniai, \epsiloni = 0 or 1. The sequence is called strongly complete if it remains complete after omitting any finite number of terms. Let M = (m1,m2, ...) be a sequence of non-negative integers. SM is a sequence which contains precisely mk entries equal to Fk where Fk is the k-th term of the Fibonacci sequence. Put \tau = (1+\sqrt 5)/2. The authors prove that if (2) sum ook = 1mk \tau -k < oo then SM is not strongly complete but if the series (2) diverges and mk \tau -k is monotone then it is strongly complete.
Classif.: * 11B39 Special numbers, etc.
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