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 A005203 Fibonacci numbers (or rabbit sequence) converted to decimal. (Formerly M1539) 17
 0, 1, 2, 5, 22, 181, 5814, 1488565, 12194330294, 25573364166211253, 439347050970302571643057846, 15829145720289447797800874537321282579904181, 9797766637414564027586288536574448245991597197836000123235901011048118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is also the denominator of the continued fraction [2^F(0), 2^F(1), 2^F(2), 2^F(3), 2^F(4), ..., 2^F(n-1)] for n>0. For the numerator, see A063896. - Chinmay Dandekar and Greg Dresden, Sep 11 2020 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..17 J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc., 63 (1977), 29-32. H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., Sequences associated with t-ary coding of Fibonacci's rabbits, Fib. Quart., 15 (1977), 311-318. Ron Knott, The Fibonacci Rabbit Sequence Ron Knott, Rabbit Sequence in Zeckendorf Expansion (A003714) Eric Weisstein's World of Mathematics, Rabbit Sequence FORMULA a(0) = 0, a(1) = 1, a(n) = a(n-1) * 2^F(n-1) + a(n-2). a(n) = rewrite_0to1_1to10_n_i_times(0, n) [ Each 0->1, 1->10 in binary expansion ] MAPLE rewrite_0to1_1to10_n_i_times := proc(n, i) local z, j; z := n; j := i; while(j > 0) do z := rewrite_0to1_1to10(z); j := j - 1; od; RETURN(z); end; rewrite_0to1_1to10 := proc(n) option remember; if(n < 2) then RETURN(n + 1); else RETURN(((2^(1+(n mod 2))) * rewrite_0to1_1to10(floor(n/2))) + (n mod 2) + 1); fi; end; MATHEMATICA a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n-1]*2^Fibonacci[n-1] + a[n-2]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jul 27 2011 *) CROSSREFS Cf. A000045, A048707, A003714, A048721, A048722, A048678, A048679, A048680, A005205, A063896. Column k=2 of A144287. Sequence in context: A361331 A342967 A042933 * A193660 A090450 A137099 Adjacent sequences: A005200 A005201 A005202 * A005204 A005205 A005206 KEYWORD nonn,base AUTHOR N. J. A. Sloane EXTENSIONS Comments and more terms from Antti Karttunen, Mar 30 1999 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)