A116941 Permutation of the natural numbers in conjunction with A116939 and A003056.

0, 1, 3, 2, 4, 6, 5, 7, 9, 11, 8, 10, 12, 14, 16, 13, 15, 17, 19, 21, 23, 18, 20, 22, 24, 26, 28, 30, 25, 27, 29, 31, 33, 35, 37, 39, 32, 34, 36, 38, 40, 42, 44, 46, 48, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 61, 63, 65, 67, 69, 71, 73

Offset: 0

Author

Reinhard Zumkeller, Feb 27 2006

Keywords

• nonn

Comments

Inverse: A116942;

A003056(n) = A116939(a(n)).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences that are permutations of the natural numbers

Programs

Haskell

a116941 n = a116941_list !! n
a116941_list = f 0 1 (zip a116939_list [0..]) [] where
   f u v xis'@((x,i):xis) ws
     | x == u    = i : f u v xis ws
     | x == v    = f u v xis (i : ws)
     | otherwise = reverse ws ++ f v x xis' []
-- Reinhard Zumkeller, Jun 28 2013

Mathematica

Table[ Ceiling[(n -1)^2/2] + 2k -2, {n, 12}, {k, n}] // Flatten (* Robert G. Wilson v, Mar 09 2017 after Ivan Neretin in A074147 *)

Formula

a(n) = A074147(n+1) - 1. - Robert G. Wilson v, Mar 09 2017