Voozh

A339213

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

1, 3, 6, 10, 12, 15, 19, 23, 26, 30, 32, 38, 41, 43, 52, 55, 59, 61, 64, 68, 72, 75, 79, 81, 86, 89, 91, 97, 101, 104, 108, 110, 115, 118, 120, 126, 131, 135, 137, 140, 144, 148, 151, 155, 157, 163, 166, 168, 177, 180, 184, 186, 189, 193, 197, 200, 204, 206, 213

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

REFERENCES

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

F. Michel Dekking, The sum of digits function of the base phi expansion of the natural numbers, arXiv:1911.10705 [math.NT], 2019.

Ron Knott, Using Powers of Phi to represent Integers (Base Phi).

Eric Weisstein's World of Mathematics, Self Number.