A215501 Inverse of permutation in A215366.

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 13, 11, 20, 14, 15, 12, 31, 16, 46, 17, 21, 22, 68, 18, 23, 32, 24, 25, 98, 26, 140, 19, 33, 47, 34, 27, 196, 69, 48, 28, 273, 35, 374, 36, 37, 99, 509, 29, 49, 38, 70, 50, 685, 39, 51, 40, 100, 141, 916, 41, 1213, 197, 52, 30

Offset: 1

Author

Alois P. Heinz, Aug 13 2012

Keywords

• nonn
• look

Comments

Permutation of the natural numbers A000027 with fixed points 1-6, 9, 10, 14, 15, 21, 22, 33, 49, 1095199, ... and inverse permutation A215366 (with offset 1).

Links

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

Crossrefs

Cf. A000027, A000040, A000070, A000079, A056239, A215366.

Programs

Maple

g:= proc(n, i) option remember; `if`(n=0 or i<2, [2^n], [seq(
      map(p->p*ithprime(i)^j, g(n-i*j, i-1))[], j=0..n/i)]) end:
b:= proc() local l, i; l:=[]; i:=0;
      proc(n) while nops(l)
				

Mathematica

g[n_, i_] := g[n, i] = If[n == 0 || i < 2, {2^n}, Flatten[ Table[ #*Prime[i]^j& /@ g[n - i*j, i - 1], {j, 0, n/i}]]];
b[n_] := Module[{l, i}, l = {}; i = 0; While[Length[l] < n, l = Join[l, Sort[g[i, i]]]; i++]; l[[n]]];
a[n_] := Module[{t, a}, t = 0; a[_] = -1; Module[{h}, While[a[n] == -1, t++; h = b[t]; If[a[h] == -1, a[h] = t]]]; a[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 14 2023, after Alois P. Heinz *)

Formula

a(n) = A000070(A056239(n)-1)+1 for n in A000040.

a(n) = A000070(A056239(n)) for n in A000079.

A000070(A056239(n)-1) < a(n) <= A000070(A056239(n)).