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 A117407 a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732). 0
 1, 2, 1, 3, 4, 5, 2, 6, 7, 3, 8, 9, 10, 4, 11, 12, 13, 5, 14, 15, 6, 16, 17, 18, 7, 19, 20, 8, 21, 22, 23, 9, 24, 25, 26, 10, 27, 28, 11, 29, 30, 31, 12, 32, 33, 34, 13, 35, 36, 14, 37, 38, 39, 15, 40, 41, 16, 42, 43, 44, 17, 45, 46, 47, 18, 48, 49, 19, 50, 51, 52, 20, 53, 54, 21, 55 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Every positive integer occurs exactly twice. Taking a Lucas number (A000032) of terms L(n) starting at a(0), the last two terms are a pair of Fibonacci numbers (A000045). If n is even, then the last two terms are F(n+1) followed by F(n-1), if n is odd they are F(n-1) followed by F(n+1), where F is the Fibonacci sequence. For example, the first L(4) = 7 terms of this sequence are (1,2,1,3,4,5,2) and the last members are 5 and 2 which are equal to F(5) and F(3). Note also that L(n) = F(n-1) + F(n+1). LINKS EXAMPLE a(9) = 3 because 9 = T(3). CROSSREFS Cf. A026272, A026242. Sequence in context: A318311 A284584 A256100 * A232095 A279436 A082470 Adjacent sequences:  A117404 A117405 A117406 * A117408 A117409 A117410 KEYWORD nonn AUTHOR Casey Mongoven, Mar 13 2006 STATUS approved

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Last modified August 8 01:38 EDT 2020. Contains 336285 sequences. (Running on oeis4.)