This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362716 #20 May 05 2023 01:34:00
%S A362716 0,1,1,1,2,1,2,1,2,2,2,3,1,2,2,3,2,3,1,2,2,2,3,2,3,2,3,3,3,4,1,2,2,3,
%T A362716 2,3,2,3,3,3,4,2,3,3,4,3,4,1,2,2,2,3,2,3,2,3,3,3,4,2,3,3,4,3,4,2,3,3,
%U A362716 3,4,3,4,3,4,4,4,5,1,2,2,3,2,3,2,3,3,3
%N A362716 Sum of the bits of the "integer part" of the base-phi representation of n.
%C A362716 The phi-representation of n is the (essentially) unique way to write n = Sum_{j=L..R} b(j)*phi^j, where b(j) is in {0,1} and -oo < L <= 0 <= R, where phi = (1+sqrt(5))/2, subject to the condition that b(j)b(j+1) != 1. The "integer" part is the string of bits b(R)b(R-1)...b(1)b(0).
%H A362716 George Bergman, <a href="https://math.berkeley.edu/~gbergman/papers/base_tau.pdf">A number system with an irrational base</a>, Math. Mag. 31 (1957), 98-110.
%H A362716 Jeffrey Shallit, <a href="https://arxiv.org/abs/2305.02672">Proving Properties of phi-Representations with the Walnut Theorem-Prover</a>, arXiv:2305.02672 [math.NT], 2023.
%F A362716 There is a linear representation of rank 19 for a(n).
%e A362716 For n = 20 we have n = phi^6 + phi^1 + phi^(-2) + phi^(-6), and the "integer part" has 2 terms, so a(20) = 2.
%Y A362716 Cf. A055778.
%K A362716 nonn
%O A362716 0,5
%A A362716 _Jeffrey Shallit_, Apr 30 2023