A117770 Fibonacci numbers for which the product of the digits is also a Fibonacci number.

0, 1, 2, 3, 5, 8, 13, 21, 610, 10946, 75025, 832040, 2178309, 5702887, 14930352, 39088169, 102334155, 165580141, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099

Offset

1,3

Comments

A000045 INTERSECT A011540 is a subsequence. As a consequence of Carmichael's theorem, the product of the digits of terms in the sequence must be in the set {0, 1, 2, 3, 5, 8, 21, 144} and if a term is zeroless (A052382), then at most 6 digits are not equal to 1. Conjecture: all terms > 21 have a 0 digit, i.e. is a member of A011540. - Chai Wah Wu, Mar 12 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Example

21 is in the sequence because (1)it is a Fibonacci number and (2)the product of its digits 2*1=2 is also a Fibonacci number.

Mathematica

With[{fibs=Fibonacci[Range[0, 100]]}, Select[fibs, MemberQ[fibs, Times@@ IntegerDigits[ #]]&]]//Union (* Harvey P. Dale, Aug 27 2016 *)

Prog

(Python)
from operator import mul
from functools import reduce
A117770_list, a, b = [0], 1, 1
for i in range(10**3):
    if reduce(mul, (int(d) for d in str(b))) in (0, 1, 2, 3, 5, 8, 21, 144):
        A117770_list.append(b)
    a, b = b, a+b # Chai Wah Wu, Mar 13 2016

Crossrefs

Cf. A000045, A117769.

Sequence in context: A042339 A137574 A041247 * A053412 A198202 A349840

Adjacent sequences: A117767 A117768 A117769 * A117771 A117772 A117773

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Extensions

Entries checked by Klaus Brockhaus, Apr 17 2006

Status

approved