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A339213 Phi-base self numbers: positive numbers not of the form k + A055778(k). 8
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.

Wikipedia, Golden ratio base.

Wikipedia, Self number.

Index entries for Colombian or self numbers and related sequences

MATHEMATICA

s[1] = 2; s[n_] := n + Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[Log[GoldenRatio, n]]][[1]]; m = 220; Complement[Range[m], Array[s, m]]

CROSSREFS

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

Sequence in context: A319452 A187744 A007960 * A280243 A032732 A187352

Adjacent sequences:  A339210 A339211 A339212 * A339214 A339215 A339216

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Nov 27 2020

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)