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A117769 Lucas numbers for which the product of the digits is a Fibonacci number. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 5 00:21 EST 2021. Contains 349530 sequences. (Running on oeis4.)