A117769 Lucas numbers for which the product of the digits is a Fibonacci number.

1, 3, 11, 18, 2207, 39603, 64079, 103682, 439204, 710647, 1860498, 3010349, 4870847, 12752043, 20633239, 54018521, 87403803, 370248451, 599074578, 969323029, 1568397607, 2537720636, 4106118243, 10749957122, 17393796001

Offset

1,2

Comments

A000204 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 > 18 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

18 is in the sequence because (1)it is a Lucas number and (2)the product of its digits 1*8=8 is a Fibonacci number.

Mathematica

lim=50; fn=Table[Fibonacci[k], {k, 0, lim}] ; ln=Table[LucasL[n, 1], {n, lim}] ; Select[ln, MemberQ[fn, Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)

Prog

(Python)
from operator import mul
from functools import reduce
A117769_list, a, b = [], 2, 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):
        A117769_list.append(b)
    a, b = b, a+b # Chai Wah Wu, Mar 13 2016

Crossrefs

Cf. A000045, A000204, A117770.

Sequence in context: A335135 A228470 A246453 * A252802 A030377 A092060

Adjacent sequences: A117766 A117767 A117768 * A117770 A117771 A117772

Keyword

base,nonn

Author

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

Extensions

a(24) corrected and offset changed by Chai Wah Wu, Mar 12 2016

Status

approved