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 A112310 Number of terms in lazy Fibonacci representation of n. 9
 0, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 5, 6, 4, 4, 5, 4, 5, 5, 5, 6, 4, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 7, 4, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 7, 5, 5, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 8, 5, 5, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 7, 6, 6, 7, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Equivalently, the number of ones in the maximal Fibonacci bit-representation (A104326) of n. Conjecture: if we split the sequence in groups that contain Fibonacci(k) terms like (0), (1), (1, 2), (2, 2, 3), (2, 3, 3, 3, 4), (3, 3, 4, 3, 4, 4, 4, 5) etc, the sums in the groups are the terms of A023610. - Gary W. Adamson, Nov 02 2010 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 J. L. Brown, Jr., A new characterization of the Fibonacci numbers, Fibonacci Quarterly 3, no. 1 (1965) 1-8. W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, Fib. Q., 43 (No. 1, 2005), 60-69. EXAMPLE a(10) = 3 because A104326(10) = 1110 contains three ones. MATHEMATICA DeleteCases[IntegerDigits[Range[200], 2], {___, 0, 0, ___}] A112309 = Map[DeleteCases[Reverse[#] Fibonacci[Range[Length[#]] + 1], 0] &, DeleteCases[IntegerDigits[-1 + Range[200], 2], {___, 0, 0, ___}]] A112310 = Map[Length, A112309] (* Peter J. C. Moses, Mar 03 2015 *) PROG (Haskell) a112310 n = a112310_list !! n a112310_list = concat fss where    fss = [0] : [1] : (map (map (+ 1))) (zipWith (++) fss \$ tail fss) -- Reinhard Zumkeller, Oct 26 2013 CROSSREFS Number of terms in row n of A112309. Cf. A117479, A035517, A104326, A007895. Record positions are in A001911. - Ray Chandler, Dec 01 2005 Sequence in context: A128330 A133801 A181630 * A137734 A182210 A078705 Adjacent sequences:  A112307 A112308 A112309 * A112311 A112312 A112313 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 01 2005 EXTENSIONS Extended by Ray Chandler, Dec 01 2005 Merged with a sequence from Casey Mongoven, Mar 20 2006, by Franklin T. Adams-Watters, Dec 19 2006 STATUS approved

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Last modified October 21 14:56 EDT 2019. Contains 328301 sequences. (Running on oeis4.)