A225850 Inverse of permutation in A167151.

0, 1, 2, 3, 4, 6, 8, 5, 10, 12, 14, 16, 7, 18, 20, 22, 24, 26, 9, 28, 30, 32, 34, 36, 38, 40, 11, 42, 44, 46, 48, 50, 52, 54, 56, 13, 58, 60, 62, 64, 66, 68, 70, 72, 74, 15, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 17, 96, 98, 100, 102, 104, 106, 108, 110, 112

Offset: 0

Author

Reinhard Zumkeller, May 17 2013

Keywords

• nonn

Comments

For n > 0: a(A005228(n)) = 2*n-1 and a(A030124(n)) = 2*n.

For n > 0: A232739(n) = a(A232739(n+1))/2. - Antti Karttunen, Dec 04 2013

Links

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

Crossrefs

Inverse permutation: A167151.

Cf. also A005228, A030124, A232739, A232746, A232747, A232749, and also the permutation pair A232751/A232752.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a225850 = fromJust . (`elemIndex` a167151_list)

Mathematica

nmax = 100; A5228 = {1};
Module[{d = 2, k = 1}, Do[While[MemberQ[A5228, d], d++]; k += d; d++; AppendTo[A5228, k], {n, 1, nmax}]];
a46[n_] := For[k = 1, True, k++, If[A5228[[k]] > n, Return[k - 1]]];
a47[n_] := If[n == 1, 1, a46[n] (a46[n] - a46[n - 1])];
a48[n_] := a48[n] = If[n == 1, 0, a48[n-1] + (1 - (a46[n] - a46[n-1]))];
a49[n_] := If[n == 1, 0, a48[n] (a48[n] - a48[n - 1])];
a[n_] := If[n < 3, n, 2 (a47[n] + a49[n]) - (a46[n] - a46[n - 1])];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 09 2021 *)

Scheme

(define (A225850 n) (if (< n 3) n (- (* 2 (+ (A232747 n) (A232749 n))) (- (A232746 n) (A232746 (- n 1))))))
;; Antti Karttunen, Dec 04 2013

Formula

If n < 3, a(n) = n, otherwise a(n) = (2*(A232747(n)+A232749(n))) - (A232746(n)-A232746(n-1)). - Antti Karttunen, Dec 04 2013