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

Author

Leroy Quet, Jan 13 2005

Keywords

• nonn
• nice

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

Crossrefs

Cf. A101438 (inverse).

Programs

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

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