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 A099267 Numbers generated by the golden sieve. 11
 2, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 78, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 103, 105, 107, 108, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let f(n) denote the n-th term of the current working sequence. Start with the positive integers: 1,2,3,4,5,6,7,8,9,10,11,12,... Delete the term in position f(1), which is f(f(1))=f(1)=1, leaving: 2,3,4,5,6,7,8,9,10,11,12,... Delete the term in position f(2), which is f(f(2))=f(3)=4, leaving: 2,3,5,6,7,8,9,10,11,12,... Delete the term in position f(3), which is f(f(3))=f(5)=7, leaving: 2,3,5,6,8,9,10,11,12,... Delete the term in position f(4), which is f(f(4))=f(6)=9, leaving: 2,3,5,6,8,10,11,12,... Iterating the "sieve" indefinitely produces the sequence: 2,3,5,6,8,10,11,13,14,16,18,19,21,23,24,26,27,29,31,32,34,35,37,39,... The subsequence of primes in this sequence begins: 2, 3, 5, 11, 13, 19, 23, 29, 31, 37, 47, 53, 61, 71, 73, 79, 89, 97, 103, 107. - Jonathan Vos Post, Apr 25 2010 Positions of 1 in A189479. - Clark Kimberling, Apr 22 2011 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = floor(n*phi + 2 - phi) where phi = (1 + sqrt(5))/2. a(a(...a(1)...)) with n iterations equals F(n+1) = A000045(n+1). For n>0 and k>0 we have a(a(n) + F(k) - (1 + (-1)^k)/2) = a(a(n)) + F(k+1) - 1 - (-1)^k. - Benoit Cloitre, Nov 22 2004 a(n) = a(a(n)) - n. - Marc Morgenegg, Sep 23 2019 MATHEMATICA t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0, 1}}] &, {0}, 6] (*A189479*) Flatten[Position[t, 0]] (*A007066*) Flatten[Position[t, 1]] (*A099267*) PROG (Haskell) a099267 n = a099267_list !! (n-1) a099267_list = f 1 [1..] 0 where    f k xs y = ys' ++ f (k+1) (ys ++ xs') g where      ys' = dropWhile (< y) ys      (ys, _:xs') = span (< g) xs      g = xs !! (h - 1)      h = xs !! (k - 1) -- Reinhard Zumkeller, Sep 18 2011 CROSSREFS Numbers n such that a(n+1)-a(n)=2 are given by A004956. If prefixed by an initial 1, same as A026355. Cf. A001622, A136119, A007066, A189479. Complement of A007066. - Gerald Hillier, Dec 19 2008 Cf. A193213 (primes). Sequence in context: A260396 A029921 A026355 * A007067 A186322 A092979 Adjacent sequences:  A099264 A099265 A099266 * A099268 A099269 A099270 KEYWORD nonn,easy,nice AUTHOR Benoit Cloitre, Nov 15 2002 STATUS approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)