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A028841 Iterated sum of digits of n is a Fibonacci number. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A028770 A321702 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

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Last modified March 7 14:53 EST 2021. Contains 341897 sequences. (Running on oeis4.)