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

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, 67, 71, 76, 80, 85, 94, 100, 101, 102, 104, 107, 110, 111, 113, 116, 120, 122, 125, 131, 134, 139, 140, 143, 148, 152, 157, 161, 166, 170, 175, 184, 193, 200, 201, 203, 206

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

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

The subsequence of Fibonacci numbers begins: 0, 1, 2, 3, 5, 8, 21, 233, ... (no more up to 100000). - Dario Piazzalunga, Jan 03 2013

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A007953, A028841, A028890.

Programs

Maple

isA000045 := proc(n)
    local i,f;
    for i from 0 do
        f := combinat[fibonacci](i) ;
        if f = n then
            return true;
        elif f > n then
            return false;
        end if;
    end do:
end proc:
isA028840 := proc(n)
    isA000045(A007953(n)) ;
end proc:
for n from 0 to 1000 do
    if isA028840(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Apr 17 2013
# second Maple program:
q:= proc(n) option remember; (t->
      issqr(t+4) or issqr(t-4))(5*n^2)
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 0, 1+a(n-1)) while not q(
      add(i, i=convert(k, base, 10))) do od; k
    end:
seq(a(n), n=1..66);  # Alois P. Heinz, Jan 28 2020

Mathematica

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 *)

Extensions

More terms from Erich Friedman

0 inserted by Dario Piazzalunga, Jan 03 2013