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

0,3

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

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

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 *)

Prog

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a225850 = fromJust . (`elemIndex` a167151_list)
(Scheme)
(define (A225850 n) (if (< n 3) n (- (* 2 (+ (A232747 n) (A232749 n))) (- (A232746 n) (A232746 (- n 1))))))
;; Antti Karttunen, Dec 04 2013

Crossrefs

Inverse permutation: A167151.

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

Sequence in context: A277905 A257802 A369271 * A038150 A182831 A257725

Adjacent sequences: A225847 A225848 A225849 * A225851 A225852 A225853

Keyword

nonn

Author

Reinhard Zumkeller, May 17 2013

Status

approved