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A117770
Fibonacci numbers for which the product of the digits is also a Fibonacci number.
2
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
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
Sequence in context: A042339 A137574 A041247 * A053412 A198202 A349840
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006
EXTENSIONS
Entries checked by Klaus Brockhaus, Apr 17 2006
STATUS
approved