This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A035612 Horizontal para-Fibonacci sequence: says which column of Wythoff array (starting column count at 1) contains n. 7
 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) = 2 + n_{a(n)+2} + 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_{a(n)+2} is the digit in position a(n)+2 of 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] = {1}; f[2] = {1, 2}; f[n_] := f[n] = Join[f[n-1], Most[f[n-2]], {n}]; f[11](* 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: A138967 A274913 A265105 * A199539 A089555 A098554 Adjacent sequences:  A035609 A035610 A035611 * A035613 A035614 A035615 KEYWORD nonn,nice,easy AUTHOR J. H. Conway, N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.