A339213 - OEIS

%I #14 Jun 28 2026 15:48:16

%S 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 86,89,91,97,101,104,108,110,115,118,120,126,131,135,137,140,144,148,

%U 151,155,157,163,166,168,177,180,184,186,189,193,197,200,204,206,213

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

%C Analogous to self numbers (A003052) using base phi (A130600) instead of base 10.

%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.

%H Amiram Eldar, <a href="/A339213/b339213.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 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 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SelfNumber.html">Self Number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Self_number">Self number</a>.

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%t 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 Cf. A003052, A010061, A010064, A010067, A010070, A055778, A130600, A331083, A334308, A339211, A339212, A339214, A339215.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Nov 27 2020