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 A049997 Numbers of the form Fibonacci(i)*Fibonacci(j). 17
 0, 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, 610, 699, 712, 714, 715, 720, 754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS It follows from Atanassov et al. that a(n) << sqrt(phi)^n, which matches the trivial a(n) >> sqrt(phi)^n up to a constant factor. - Charles R Greathouse IV, Feb 06 2013 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 K. T. Atanassov, Ron Knott, Kiyota Ozeki, A. G. Shannon, and László Szalay, Inequalities among related pairs of Fibonacci numbers, Fibonacci Quarterly 41:1 (2003), pp. 20-22. Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly 42:1 (2004), pp. 28-35. EXAMPLE 25 is in the sequence since it is the product of two, not necessarily distinct, Fibonacci numbers, 5 and 5. 26 is in the sequence since it is the product of two Fibonacci numbers, 2 and 13. 27 is not in the sequence because there is no way whatsoever to represent it as the product of exactly two Fibonacci numbers. MATHEMATICA Take[ Union@Flatten@Table[ Fibonacci[i]Fibonacci[j], {i, 0, 16}, {j, 0, i}], 61] (* Robert G. Wilson v, Dec 14 2005 *) PROG (PARI) list(lim)=my(phi=(1+sqrt(5))/2, v=vector(log(lim*sqrt(5))\log(phi), i, fibonacci(i+1)), u=List(), t); for(i=1, #v, for(j=i, #v, t=v[i]*v[j]; if(t>lim, break, listput(u, t)))); vecsort(Vec(u), , 8) \\ Charles R Greathouse IV, Feb 05 2013 CROSSREFS Subsequence of A065108; apart from the first term, subsequence of A094563. Complement is A228523. See A049998 for further information about this sequence. Cf. A080097. Intersection with A059389 (sums of two Fibonacci numbers) is A226857. Cf. also A090206, A005478. Sequence in context: A052347 A193299 A022773 * A226857 A256007 A324689 Adjacent sequences:  A049994 A049995 A049996 * A049998 A049999 A050000 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)