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

0,3

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

Formula

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A049831 A186005 A080782 * A166695 A254107 A116942

Adjacent sequences: A116938 A116939 A116940 * A116942 A116943 A116944

Keyword

nonn

Author

Reinhard Zumkeller, Feb 27 2006

Status

approved