A065037 Inverse permutation to A036552.

1, 2, 3, 5, 7, 4, 9, 6, 11, 8, 13, 15, 17, 10, 19, 21, 23, 12, 25, 27, 29, 14, 31, 16, 33, 18, 35, 37, 39, 20, 41, 22, 43, 24, 45, 47, 49, 26, 51, 28, 53, 30, 55, 57, 59, 32, 61, 63, 65, 34, 67, 69, 71, 36, 73, 38, 75, 40, 77, 79, 81, 42, 83, 85, 87, 44, 89, 91, 93, 46, 95, 48

Offset: 1

Author

N. J. A. Sloane, Nov 05 2001

Keywords

• nonn
• easy

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. A036552, A003159, A036554, A091297.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a065037 = (+ 1) . fromJust . (`elemIndex` a036552_list)
-- Reinhard Zumkeller, Jan 08 2013

Formula

a(2n+1) - a(2n-1) = 2*A091297(2n-1) + 2. - Philippe Deléham, Feb 24 2004

From Philippe Deléham, Feb 24 2004: (Start)

a(2n) < a(2n+2) if a(2n+1) - a(2n-1) = 2;

a(2n) > a(2n+2) if a(2n+1) - a(2n-1) = 4.

a(n) = a(n+1) - 2 = a(n-1) + 2 iff n = 2*A036554(k) = 4*A003159(k). (End)

Extensions

More terms from Naohiro Nomoto, Nov 22 2001

Incorrect equation removed from a formula by Peter Munn, Dec 11 2020