A257797 -id:A257797 - cp's OEIS frontend

A220347 Permutation of natural numbers: a(1) = 1, a(triangular(n)) = (2a(n))-1, a(nontriangular(n)) = 2n, 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

Reinhard Zumkeller, Dec 12 2012

nonn

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

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

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.

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

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 *)

;; 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

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

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

A257798 Permutation of natural numbers: a(1) = 1; a(2n) = nontriangular(a(n)), a(2n+1) = triangular(1+a(n)), where triangular = A000217, nontriangular = A014132.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 10, 7, 15, 9, 28, 8, 21, 14, 66, 11, 36, 20, 136, 13, 55, 35, 435, 12, 45, 27, 253, 19, 120, 77, 2278, 16, 78, 44, 703, 26, 231, 152, 9453, 18, 105, 65, 1596, 43, 666, 464, 95266, 17, 91, 54, 1081, 34, 406, 275, 32385, 25, 210, 135, 7381, 89, 3081, 2345, 2598060, 22, 153, 90, 3160, 53, 1035, 740, 248160, 33

Offset: 1

Antti Karttunen, May 18 2015

nonn

This sequence can be represented as a binary tree. Each left hand child is produced as A014132(n) and each right hand child as A000217(1+n), when a parent contains n >= 1:
                                    1
                 ................../ \..................
                2                                       3
      4......../ \........6                   5......../ \.......10
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  7       15          9       28          8       21         14       66
11 36   20  136     13 55   35  435     12 45   27  253    19  120  77 2278
etc.

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers

Inverse: A257797.
Cf. A000217, A014132.
Cf. also permutation A183079.

a(1)=1; after which: a(2n) = A014132(a(n)), a(2n+1) = A000217(a(n)+1).

cp's OEIS Frontend

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

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A257798 Permutation of natural numbers: a(1) = 1; a(2n) = nontriangular(a(n)), a(2n+1) = triangular(1+a(n)), where triangular = A000217, nontriangular = A014132.

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cp's OEIS Frontend

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.

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Programs

Haskell

Mathematica

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Formula

Extensions

A257798 Permutation of natural numbers: a(1) = 1; a(2n) = nontriangular(a(n)), a(2n+1) = triangular(1+a(n)), where triangular = A000217, nontriangular = A014132.

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Formula

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