A101369 a(2n-1) = the smallest positive integer not occurring earlier in the sequence. a(2n) = the a(2n-1)th smallest positive integer among those not occurring earlier in the sequence.
1, 2, 3, 6, 4, 9, 5, 12, 7, 16, 8, 19, 10, 23, 11, 26, 13, 30, 14, 33, 15, 36, 17, 40, 18, 43, 20, 47, 21, 50, 22, 53, 24, 57, 25, 60, 27, 64, 28, 67, 29, 70, 31, 74, 32, 77, 34, 81, 35, 84, 37, 88, 38, 91, 39, 94, 41, 98, 42, 101, 44, 105, 45, 108, 46, 111, 48, 115, 49, 118
Offset: 1
Links
Crossrefs
Cf. A101438 (inverse).
Programs
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Haskell
import Data.List (delete) a101369 n = a101369_list !! (n-1) a101369_list = f [1..] where f (x:xs) = x : y : f (delete y xs) where y = xs !! (x - 1) -- Reinhard Zumkeller, Jul 01 2013
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Mathematica
lst = Range[150]; a[n_] := a[n] = If[ OddQ[n], b = First[lst]; lst = Rest[lst]; b, b = lst[[ a[n - 1]]]; lst = Drop[lst, {a[n - 1]}]; b]; Table[ a[n], {n, 70}]
Formula
a(n)Robert G. Wilson v, Feb 11 2005
For n>0, a(2n-1)=1+floor((2n-1)/sqrt(2)) and a(2n)=2n+floor((2n)/sqrt(2)-1/sqrt(2)) - Benoit Cloitre, Feb 22 2005
Extensions
More terms from Robert G. Wilson v, Feb 11 2005
Comments