A028841 Iterated sum of digits of n is a Fibonacci number.

1, 2, 3, 5, 8, 10, 11, 12, 14, 17, 19, 20, 21, 23, 26, 28, 29, 30, 32, 35, 37, 38, 39, 41, 44, 46, 47, 48, 50, 53, 55, 56, 57, 59, 62, 64, 65, 66, 68, 71, 73, 74, 75, 77, 80, 82, 83, 84, 86, 89, 91, 92, 93, 95, 98, 100, 101, 102, 104, 107, 109, 110, 111, 113, 116, 118, 119

Offset

1,2

Comments

Intermediate iterations don't count. For example, with 85, we have 8 + 5 = 13, which is a Fibonacci number, but 1 + 3 = 4, which is not a Fibonacci numbers, so 85 is not in the sequence. - Alonso del Arte, Jan 20 2020

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1001 [Offset adapted by Georg Fischer, Feb 28 2020]

Formula

Conjectures from Colin Barker, Feb 18 2020: (Start)

G.f.: x*(1 + x + x^2 + 2*x^3 + 3*x^4 + x^5) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.

(End)

Example

98 -> 9 + 8 = 17 -> 1 + 7 = 8 is a Fibonacci number.

Mathematica

With[{fibo = {1, 2, 3, 5, 8}}, Select[Range[120], MemberQ[fibo, NestWhile[Total[IntegerDigits[#]] &, #, # > 9 &]]&]] (* Harvey P. Dale, Apr 11 2013 *)

Prog

(Scala) def fiboDRQ(n: Int): Boolean = List(1, 2, 3, 5, 8).contains(n % 9)
(1 to 100).filter(fiboDRQ) // Alonso del Arte, Jan 28 2020

Crossrefs

Cf. A010888, A028840, A028891.

Sequence in context: A321702 A351876 A028800 * A028840 A189143 A047605

Adjacent sequences: A028838 A028839 A028840 * A028842 A028843 A028844

Keyword

nonn,base

Author

N. J. A. Sloane

Extensions

More terms from Patrick De Geest, Jun 15 1999

Offset corrected to 1 by Alonso del Arte, Jan 28 2020 at Michel Marcus's suggestion

Status

approved