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A028840 Numbers k such that sum of digits of k is a Fibonacci number.

%I A028840 #19 Feb 12 2021 17:43:42
%S A028840 0,1,2,3,5,8,10,11,12,14,17,20,21,23,26,30,32,35,41,44,49,50,53,58,62,
%T A028840 67,71,76,80,85,94,100,101,102,104,107,110,111,113,116,120,122,125,
%U A028840 131,134,139,140,143,148,152,157,161,166,170,175,184,193,200,201,203,206
%N A028840 Numbers k such that sum of digits of k is a Fibonacci number.
%C A028840 The subsequence of primes begins: 2, 3, 5, 11, 17, 23, 41, 53, 67, 71, 101, 107, 113, 131, 139, 157, 193, 229, 233, 251 ... - _Dario Piazzalunga_, Jan 03 2013
%C A028840 The subsequence of Fibonacci numbers begins: 0, 1, 2, 3, 5, 8, 21, 233, ... (no more up to 100000). - _Dario Piazzalunga_, Jan 03 2013
%H A028840 Alois P. Heinz, <a href="/A028840/b028840.txt">Table of n, a(n) for n = 1..10000</a>
%p A028840 isA000045 := proc(n)
%p A028840     local i,f;
%p A028840     for i from 0 do
%p A028840         f := combinat[fibonacci](i) ;
%p A028840         if f = n then
%p A028840             return true;
%p A028840         elif f > n then
%p A028840             return false;
%p A028840         end if;
%p A028840     end do:
%p A028840 end proc:
%p A028840 isA028840 := proc(n)
%p A028840     isA000045(A007953(n)) ;
%p A028840 end proc:
%p A028840 for n from 0 to 1000 do
%p A028840     if isA028840(n) then
%p A028840         printf("%d,",n);
%p A028840     end if;
%p A028840 end do: # _R. J. Mathar_, Apr 17 2013
%p A028840 # second Maple program:
%p A028840 q:= proc(n) option remember; (t->
%p A028840       issqr(t+4) or issqr(t-4))(5*n^2)
%p A028840     end:
%p A028840 a:= proc(n) option remember; local k; for k from
%p A028840      `if`(n=1, 0, 1+a(n-1)) while not q(
%p A028840       add(i, i=convert(k, base, 10))) do od; k
%p A028840     end:
%p A028840 seq(a(n), n=1..66);  # _Alois P. Heinz_, Jan 28 2020
%t A028840 f = Union[Fibonacci[Range[0, 8]]]; t = {}; n = 0; While[c = Total[IntegerDigits[n]]; c < f[[-1]], If[MemberQ[f, c], AppendTo[t, n]]; n++]; t (* _T. D. Noe_, Jan 03 2013 *)
%Y A028840 Cf. A000045, A007953, A028841, A028890.
%K A028840 nonn,base,easy
%O A028840 1,3
%A A028840 _N. J. A. Sloane_
%E A028840 More terms from _Erich Friedman_
%E A028840 0 inserted by _Dario Piazzalunga_, Jan 03 2013