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 A118240 The part of n in base phi left of the decimal using a least-greedy algorithm representation. 3
 0, 1, 1, 10, 11, 101, 111, 1010, 1011, 1101, 1110, 1111, 10101, 10111, 11010, 11011, 11101, 11111, 101010, 101011, 101101, 101110, 101111, 110101, 110111, 111010, 111011, 111101, 111110, 111111, 1010101, 1010111, 1011010, 1011011, 1011101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Uses least-greedy algorithm (start with largest possible power of phi, writing a 1 only when required, then work downward). a(n) is also the left portion of the base-phi representation of n in Knott's representation which uses the least number of 0's, the most 1's, and in which the right-hand portion (see A362919) is finite. - N. J. A. Sloane, May 27 2023 LINKS Table of n, a(n) for n=0..34. Ron Knott, Phigits and the Base Phi representation. Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023. [Note that this document has been revised multiple times.] EXAMPLE 6 = 111.01101010... in base phi using the least-greedy algorithm. The part to the left of the decimal is a(6) = 111. PROG constant (float): phi=(sqrt(5)+1)/2; variable (float): lphi=phi^floor[log(n)/log(phi)]; variable (float): rem=n; variable (integer): count=0; loop: while lphi>1 (count=count*10; lphi=lphi/phi; if(rem > lphi*phi) { rem=rem-lphi; count++; }} CROSSREFS Cf. A055778, A104605, A118241, A105424, A362919, A362920. Sequence in context: A368804 A037090 A171676 * A157845 A230297 A086084 Adjacent sequences: A118237 A118238 A118239 * A118241 A118242 A118243 KEYWORD nonn,base AUTHOR Graeme McRae, Apr 17 2006 EXTENSIONS a(1) corrected by N. J. A. Sloane, May 27 2023 STATUS approved

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Last modified April 24 15:37 EDT 2024. Contains 371960 sequences. (Running on oeis4.)