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 A112309 Triangle read by rows: row n gives terms in lazy Fibonacci representation of n. 3
 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 5, 1, 2, 5, 1, 3, 5, 2, 3, 5, 1, 2, 3, 5, 1, 3, 8, 2, 3, 8, 1, 2, 3, 8, 2, 5, 8, 1, 2, 5, 8, 1, 3, 5, 8, 2, 3, 5, 8, 1, 2, 3, 5, 8, 2, 5, 13, 1, 2, 5, 13, 1, 3, 5, 13, 2, 3, 5, 13, 1, 2, 3, 5, 13, 1, 3, 8, 13, 2, 3, 8, 13, 1, 2, 3, 8, 13, 2, 5, 8, 13, 1, 2, 5, 8, 13, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Write n as a sum c_2 F_2 + c_3 F_3 + ..., where the F_i are Fibonacci numbers and the c_i are 0 or 1. The lazy expansion is the minimal one in the lexicographic order, in contrast to the Zeckendorf expansion (A035517, A007895), which is the maximal one. In other words we give preference to the smallest Fibonacci numbers. LINKS W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, Fib. Q., 43 (No. 1, 2005), 60-69. EXAMPLE Triangle begins: 1 meaning 1 = 1 2 meaning 2 = 2 1 2 meaning 3 = 1+2 1 3 meaning 4 = 1+3 2 3 meaning 5 = 2+3 1 2 3 meaning 6 = 1+2+3 (and not the Zeckendorf expansion 1+5) 2 5 meaning 7 = 2+5 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 *) CROSSREFS Cf. A000045, A112310, A035517, A007895. Sequence in context: A259177 A304036 A173442 * A160006 A060682 A280363 Adjacent sequences:  A112306 A112307 A112308 * A112310 A112311 A112312 KEYWORD nonn,tabf,easy AUTHOR N. J. A. Sloane, Dec 01 2005 EXTENSIONS Extended by Ray Chandler, Dec 01 2005 STATUS approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)