cp's OEIS Frontend

A339213 Phi-base self numbers: positive numbers not of the form k + A055778(k).

%I A339213 #13 Feb 16 2025 08:34:01
%S A339213 1,3,6,10,12,15,19,23,26,30,32,38,41,43,52,55,59,61,64,68,72,75,79,81,
%T A339213 86,89,91,97,101,104,108,110,115,118,120,126,131,135,137,140,144,148,
%U A339213 151,155,157,163,166,168,177,180,184,186,189,193,197,200,204,206,213
%N A339213 Phi-base self numbers: positive numbers not of the form k + A055778(k).
%C A339213 Analogous to self numbers (A003052) using base phi (A130600) instead of base 10.
%D A339213 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
%H A339213 Amiram Eldar, <a href="/A339213/b339213.txt">Table of n, a(n) for n = 1..10000</a>
%H A339213 F. Michel Dekking, <a href="https://arxiv.org/abs/1911.10705">The sum of digits function of the base phi expansion of the natural numbers</a>, arXiv:1911.10705 [math.NT], 2019.
%H A339213 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phigits.html">Using Powers of Phi to represent Integers (Base Phi)</a>.
%H A339213 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SelfNumber.html">Self Number</a>.
%H A339213 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>.
%H A339213 Wikipedia, <a href="http://en.wikipedia.org/wiki/Self_number">Self number</a>.
%H A339213 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%t A339213 s[1] = 2; s[n_] := n + Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[Log[GoldenRatio, n]]][[1]]; m = 220; Complement[Range[m], Array[s, m]]
%Y A339213 Cf. A003052, A010061, A010064, A010067, A010070, A055778, A130600, A331083, A334308, A339211, A339212, A339214, A339215.
%K A339213 nonn,base
%O A339213 1,2
%A A339213 _Amiram Eldar_, Nov 27 2020