%I #14 Mar 14 2016 03:52:38
%S 1,3,11,18,2207,39603,64079,103682,439204,710647,1860498,3010349,
%T 4870847,12752043,20633239,54018521,87403803,370248451,599074578,
%U 969323029,1568397607,2537720636,4106118243,10749957122,17393796001
%N Lucas numbers for which the product of the digits is a Fibonacci number.
%C 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
%H Chai Wah Wu, <a href="/A117769/b117769.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%o (Python)
%o from operator import mul
%o from functools import reduce
%o A117769_list, a, b = [], 2, 1
%o for i in range(10**3):
%o if reduce(mul,(int(d) for d in str(b))) in (0,1,2,3,5,8,21,144):
%o A117769_list.append(b)
%o a, b = b, a+b # _Chai Wah Wu_, Mar 13 2016
%Y Cf. A000045, A000204, A117770.
%K base,nonn
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006
%E a(24) corrected and offset changed by _Chai Wah Wu_, Mar 12 2016