A213912 -id:A213912 - cp's OEIS frontend

A213913 Inverse permutation of A213912.

1, 6, 2, 9, 5, 7, 23, 84, 3, 13, 47, 10, 27, 88, 44, 17, 51, 8, 92, 21, 24, 96, 132, 85, 105, 114, 4, 64, 36, 14, 60, 32, 48, 141, 73, 11, 56, 194, 28, 255, 155, 89, 137, 175, 45, 124, 69, 18, 270, 449, 52, 146, 78, 280, 199, 190, 93, 225, 180, 22, 129, 251

Offset: 1

Reinhard Zumkeller, Mar 05 2013

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a213913 = (+ 1) . fromJust . (`elemIndex` a213912_list)

A335836 a(1) = 1; for n>1, a(n) = floor(a(n-1)^(1/3)) if that number is not already in the sequence, otherwise a(n) = 2*a(n-1).

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 3, 6, 12, 24, 48, 96, 192, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 13, 26, 52, 104, 208, 416, 7, 14, 28, 56, 112, 224, 448, 896, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 33, 66, 132, 264, 528, 1056, 2112

Offset: 1

Jinyuan Wang, Jun 27 2020

nonn

If k is not in this sequence, then none of k^(3^t), k^(3^t)+1, ..., (k+1)^(3^t)-1 belong to the sequence. Because (k+1)^(3^k) > 2*k^(3^k), any m > k^(3^k) is not in the sequence, which is a contradiction to {a(n)} is not bounded above. Therefore, this sequence is a permutation of the natural numbers.

Cf. A048766, A114183, A213912.

Nest[Append[#1, If[FreeQ[#1, #2], #2, 2 #1[[-1]] ]] & @@ {#, Floor[#[[-1]]^(1/3)]} &, {1}, 56] (* Michael De Vlieger, Jun 28 2020 *)

lista(nn) = {my(k, v=vector(nn)); v[1]=1; for(n=2, nn, if(vecsearch(vecsort(v), k=sqrtnint(v[n-1], 3)), v[n]=2*v[n-1], v[n]=k)); v; }

cp's OEIS Frontend

A213913 Inverse permutation of A213912.

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A335836 a(1) = 1; for n>1, a(n) = floor(a(n-1)^(1/3)) if that number is not already in the sequence, otherwise a(n) = 2*a(n-1).

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