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

1,2

Comments

A permutation of the positive integers.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(n)<a(n+2). - 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

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}]

Prog

(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

Crossrefs

Cf. A101438 (inverse).

Sequence in context: A059900 A123664 A084980 * A125147 A103864 A268712

Adjacent sequences: A101366 A101367 A101368 * A101370 A101371 A101372

Keyword

nonn,nice

Author

Leroy Quet, Jan 13 2005

Extensions

More terms from Robert G. Wilson v, Feb 11 2005

Status

approved