A339211 Zeckendorf self numbers: numbers not of the form k + A007895(k).

1, 5, 7, 10, 19, 21, 27, 29, 32, 36, 40, 42, 45, 54, 61, 63, 66, 75, 77, 83, 85, 88, 95, 97, 100, 109, 111, 117, 119, 122, 126, 130, 132, 135, 144, 146, 150, 152, 155, 164, 166, 172, 174, 177, 181, 185, 187, 190, 199, 206, 208, 211, 220, 222, 228, 230, 233, 239

Offset

1,2

Comments

Analogous to self numbers (A003052) using the Zeckendorf representation (A014417) instead of decimal expansion.

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

Eric Weisstein's World of Mathematics, Self Number.

Eric Weisstein's World of Mathematics, Zeckendorf Representation.

Wikipedia, Self number.

Index entries for Colombian or self numbers and related sequences

Mathematica

z[n_] := n + Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; m = 250; Complement[Range[m], Array[z, m]] (* after Alonso del Arte at A007895 *)

Crossrefs

Cf. A003052, A007895, A010061, A010064, A010067, A010070, A014417, A328208, A339212, A339213, A339214, A339215.

Sequence in context: A320447 A113194 A356103 * A088768 A131998 A141443

Adjacent sequences: A339208 A339209 A339210 * A339212 A339213 A339214

Keyword

nonn,base,changed

Author

Amiram Eldar, Nov 27 2020

Status

approved