A028891 -id:A028891 - cp's OEIS frontend

A028890 Product of digits of n is a nonzero Fibonacci number.

1, 2, 3, 5, 8, 11, 12, 13, 15, 18, 21, 24, 31, 37, 42, 51, 73, 81, 111, 112, 113, 115, 118, 121, 124, 131, 137, 142, 151, 173, 181, 211, 214, 222, 241, 289, 298, 311, 317, 368, 371, 386, 412, 421, 449, 466, 494, 511, 638, 646, 664, 683, 713, 731, 811, 829, 836

Offset: 1

N. J. A. Sloane

Numbers n whose product of digits is 1, 2, 3, 5, 8, 21, or 144 (these being the only 7-smooth Fibonacci numbers). - Robert Israel, Jan 26 2020

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007954, A028891, A028840.

select(t -> member(convert(convert(t,base,10),`*`),[1, 2, 3, 5, 8, 21, 144]),[$1..999]); # Robert Israel, Jan 26 2020

More terms from Erich Friedman.

Name clarified and offset changed by Robert Israel, Jan 26 2020

A028841 Iterated sum of digits of n is a Fibonacci number.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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

			98 -> 9 + 8 = 17 -> 1 + 7 = 8 is a Fibonacci number.

Harvey P. Dale, Table of n, a(n) for n = 1..1001 [Offset adapted by _Georg Fischer_, Feb 28 2020]

Cf. A010888, A028840, A028891.

With[{fibo = {1, 2, 3, 5, 8}}, Select[Range[120], MemberQ[fibo, NestWhile[Total[IntegerDigits[#]] &, #, # > 9 &]]&]] (* Harvey P. Dale, Apr 11 2013 *)

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

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)

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

cp's OEIS Frontend

A028890 Product of digits of n is a nonzero Fibonacci number.

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A028841 Iterated sum of digits of n is a Fibonacci number.

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