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).

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

Author

Jinyuan Wang, Jun 27 2020

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A048766, A114183, A213912.

Programs

Mathematica

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

PARI

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; }