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 A035612 Horizontal para-Fibonacci sequence: says which column of Wythoff array (starting column count at 1) contains n. 8
 1, 2, 3, 1, 4, 1, 2, 5, 1, 2, 3, 1, 6, 1, 2, 3, 1, 4, 1, 2, 7, 1, 2, 3, 1, 4, 1, 2, 5, 1, 2, 3, 1, 8, 1, 2, 3, 1, 4, 1, 2, 5, 1, 2, 3, 1, 6, 1, 2, 3, 1, 4, 1, 2, 9, 1, 2, 3, 1, 4, 1, 2, 5, 1, 2, 3, 1, 6, 1, 2, 3, 1, 4, 1, 2, 7, 1, 2, 3, 1, 4, 1, 2, 5, 1, 2, 3, 1, 10, 1, 2, 3, 1, 4, 1, 2, 5, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Ordinal transform of A003603. Removing all 1's from this sequence and decrementing the remaining numbers generates the original sequence. - Franklin T. Adams-Watters, Aug 10 2012 a(A022342(n)) > 1; a(A026274(n) + 1) = 1. - Reinhard Zumkeller, Jul 20 2015 It can be shown that a(n) is the index of the smallest Fibonacci number used in the Zeckendorf representation of n, where f(0)=f(1)=1. - Rachel Chaiser, Aug 18 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Paul Curtz, Comments on A035612, Jan 25 2016 N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98). N. J. A. Sloane, Classic Sequences FORMULA The segment between the first M and the first M+1 is given by the segment before the first M-1. a(n) = v2(A022340(n)), where v2(n) = A007814(n), the dyadic valuation of n. - Ralf Stephan, Jun 20 2004. In other words, a(n) = A007814(A003714(n)) + 1, which is certainly true. - Don Reble, Nov 12 2005 From Rachel Chaiser, Aug 18 2017: (Start) a(n) = a(p(n))+1 if n = b(p(n)) where p(n) = floor((n+2)/phi)-1 and b(n) = floor((n+1)*phi)-1 where phi=(1+sqrt(5))/2; a(n)=1 otherwise. a(n) = 3 - n_1 + s_z(n-1) - s_z(n) + s_z(p(n-1)) - s_z(p(n)), where s_z(n) is the Zeckendorf sum of digits of n (A007895), and n_1 is the least significant digit in the Zeckendorf representation of n. (End) EXAMPLE After the first 6 we see "1 2 3 1 4 1 2" then 7. MATHEMATICA f = {1}; f = {1, 2}; f[n_] := f[n] = Join[f[n-1], Most[f[n-2]], {n}]; f (* Jean-François Alcover, Feb 22 2012 *) PROG (Haskell) a035612 = a007814 . a022340 -- Reinhard Zumkeller, Jul 20 2015, Mar 10 2013 CROSSREFS Cf. A019586, A035513, A035614. Cf. A000045. Cf. A007814, A022340, A022342, A026274. Cf. A000012, A000027, A001045, A001610, A003622, A023548, A035614, A255671, A268034. Sequence in context: A274913 A330761 A265105 * A199539 A089555 A098554 Adjacent sequences:  A035609 A035610 A035611 * A035613 A035614 A035615 KEYWORD nonn,nice,easy AUTHOR J. H. Conway, N. J. A. Sloane EXTENSIONS Formula corrected by Tom Edgar, Jul 09 2018 STATUS approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)