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 A049998 a(n) = b(n)-b(n-1), where b=A049997 are numbers of the form Fibonacci(i)*Fibonacci(j). 2
 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 3, 1, 1, 8, 5, 1, 2, 13, 8, 1, 1, 3, 21, 13, 2, 1, 5, 34, 21, 3, 1, 1, 8, 55, 34, 5, 1, 2, 13, 89, 55, 8, 1, 1, 3, 21, 144, 89, 13, 2, 1, 5, 34, 233, 144, 21, 3, 1, 1, 8, 55, 377, 233, 34, 5, 1, 2, 13, 89, 610, 377, 55, 8, 1, 1, 3, 21, 144, 987, 610, 89 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS David W. Wilson conjectured (Dec 14 2005) that this sequence consists only of Fibonacci numbers. Proofs were found by Franklin T. Adams-Watters and Don Reble, Dec 14 2005. The following is Reble's proof: Rearrange A049997, as suggested by Bernardo Boncompagni: 1 2 3 4 5 6 8 9 10 13 15 16 21 24 25 26 34 39 40 42 55 63 64 65 68 89 102 104 105 110 144 165 168 169 170 178 233 267 272 273 275 288 377 432 440 441 442 445 466 Then we know that F(a+1) * F(a-1) - F(a) * F(a) = (-1)^a F(a+1) * F(b-1) - F(a-1) * F(b+1) = + (-1)^b F(a-b), if a>b = - (-1)^a F(b-a), if a

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)