%I #28 Feb 28 2020 09:52:30
%S 1,2,3,5,8,10,11,12,14,17,19,20,21,23,26,28,29,30,32,35,37,38,39,41,
%T 44,46,47,48,50,53,55,56,57,59,62,64,65,66,68,71,73,74,75,77,80,82,83,
%U 84,86,89,91,92,93,95,98,100,101,102,104,107,109,110,111,113,116,118,119
%N Iterated sum of digits of n is a Fibonacci number.
%C 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
%H Harvey P. Dale, <a href="/A028841/b028841.txt">Table of n, a(n) for n = 1..1001</a> [Offset adapted by _Georg Fischer_, Feb 28 2020]
%F Conjectures from _Colin Barker_, Feb 18 2020: (Start)
%F 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)).
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.
%F (End)
%e 98 -> 9 + 8 = 17 -> 1 + 7 = 8 is a Fibonacci number.
%t With[{fibo = {1, 2, 3, 5, 8}}, Select[Range[120], MemberQ[fibo, NestWhile[Total[IntegerDigits[#]] &, #, # > 9 &]]&]] (* _Harvey P. Dale_, Apr 11 2013 *)
%o (Scala) def fiboDRQ(n: Int): Boolean = List(1, 2, 3, 5, 8).contains(n % 9)
%o (1 to 100).filter(fiboDRQ) // _Alonso del Arte_, Jan 28 2020
%Y Cf. A010888, A028840, A028891.
%K nonn,base
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Patrick De Geest_, Jun 15 1999
%E Offset corrected to 1 by _Alonso del Arte_, Jan 28 2020 at _Michel Marcus_'s suggestion