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
KEYWORD
nonn,base
AUTHOR
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