cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A060000 If the numbers a(1)...a(n) contain a hole, then a(n+1) is the smallest hole; otherwise a(n+1) = a(n-1) + a(n).

Original entry on oeis.org

1, 2, 3, 5, 4, 9, 6, 7, 8, 15, 10, 11, 12, 13, 14, 27, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 99, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
Offset: 1

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Author

Rainer Rosenthal, Mar 09 2001

Keywords

Comments

Let H be the set of positive numbers less than a(n) which are not equal to some a(i), i < n. This H is the 'set of holes so far'. If H is nonempty, then define a(n+1) = minimum(H). Otherwise define a(n+1) = a(n-1) + a(n).
Permutation of the natural numbers with inverse A099424.
A060013(n+1) = a(A060013(n)+1). - Reinhard Zumkeller, Mar 04 2008

Crossrefs

Programs

  • Haskell
    a060000 n = a060000_list !! (n-1)
    a060000_list = 1 : 2 : f 1 2 2 [] where
       f x y m []     = z : f y z z [m+1..z-1] where z = x + y
       f x y m (h:hs) = h : f y h m hs
    -- Reinhard Zumkeller, Sep 22 2011
  • Mathematica
    h = {1, 2}; a = 1; b = 2; Do[ g = Sort[ h ]; If[ g[ [ -1 ] ] + 1 == n, c = a + b, k = 1; While[ g[ [ k ] ] == k, k++ ]; c = k ]; a = b; b = c; h = Append[ h, c ], { n, 3, 100} ]; h
    (* faster program *) h = {1, 2, 3, 5, 4, 9}; lastSum = 9; Do[AppendTo[h, If[ ++akt < lastSum, akt, ++akt; lastSum = 2*lastSum - 3]], {akt, 5, 100}]; h (* Alfred Heiligenbrunner, Jun 05 2004 *)

Formula

a(k)=k-1 if k>=7 and k <> 2^m * 3 + 4; a(k)=(k-1)*2-3 if k>=7 and k == 2^m * 3 + 4. - Alfred Heiligenbrunner, Jun 08 2004

Extensions

More terms from Robert G. Wilson v and Larry Reeves (larryr(AT)acm.org), Mar 15 2001
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