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

1,2

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

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)).

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)<n do
        l:=[l[], sort(g(i, i))[]]; i:=i+1 od; l[n]
      end
    end():
a:= proc() local t, a; t, a:= 0, proc() -1 end;
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1; h:= b(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=1..100);

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 *)

Crossrefs

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

Sequence in context: A345253 A358141 A266196 * A117333 A368577 A361376

Adjacent sequences: A215498 A215499 A215500 * A215502 A215503 A215504

Keyword

nonn,look

Author

Alois P. Heinz, Aug 13 2012

Status

approved