A220347 Permutation of natural numbers: a(1) = 1, a(triangular(n)) = (2*a(n))-1, a(nontriangular(n)) = 2*n, where triangular = A000217, nontriangular = A014132.

1, 2, 3, 4, 6, 5, 8, 12, 10, 7, 16, 24, 20, 14, 11, 32, 48, 40, 28, 22, 9, 64, 96, 80, 56, 44, 18, 15, 128, 192, 160, 112, 88, 36, 30, 23, 256, 384, 320, 224, 176, 72, 60, 46, 19, 512, 768, 640, 448, 352, 144, 120, 92, 38, 13, 1024, 1536, 1280, 896, 704, 288

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2012

Keywords

• nonn

Comments

Inverse permutation of A183079, when seen as a flattened sequence.

Links

• Reinhard Zumkeller (first 250 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10440
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A183079.

Cf. A000217, A002024, A010054, A014132, A083920, A220348.

Cf. also a similar permutation A257797 from which this differs for the first time at n=15, where a(15) = 11, while A257797(15) = 9.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a220347 =  (+ 1) . fromJust . (`elemIndex` a183079_list)

Mathematica

a[n_] := a[n] = With[{r = (-1 + Sqrt[8n + 1])/2}, Which[n <= 1, n, IntegerQ[r], 2 a[Floor[Sqrt[2n] + 1/2]] - 1, True, 2 a[n - Floor[r]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 05 2021 *)

Scheme

;; With memoizing definec-macro.
(definec (A220347 n) (cond ((<= n 1) n) ((zero? (A010054 n)) (* 2 (A220347 (A083920 n)))) (else (+ -1 (* 2 (A220347 (A002024 n)))))))
;; Antti Karttunen, May 18 2015

Formula

a(1) = 1; for n > 1: if A010054(n) = 1 [i.e., if n is triangular], then a(n) = (2*a(A002024(n)))-1, otherwise a(n) = 2*a(A083920(n)). - Antti Karttunen, May 18 2015

Extensions

Old name moved to comments by Antti Karttunen, May 18 2015