A226532 -id:A226532 - cp's OEIS frontend

A226569 Inverse permutation to A226532.

1, 2, 6, 4, 15, 3, 35, 8, 36, 30, 77, 24, 143, 70, 10, 16, 221, 72, 323, 60, 210, 154, 437, 12, 225, 286, 216, 140, 667, 5, 899, 32, 462, 442, 21, 9, 1147, 646, 858, 120, 1517, 105, 1763, 308, 540, 874, 2021, 96, 1225, 450, 1326, 572, 2491, 108, 1155, 280

Offset: 1

Reinhard Zumkeller, Jun 11 2013

Cf. A000079 (fixed points).

-- import Data.List (elemIndex); import Data.Maybe (fromJust)
a226569 = (+ 1) . fromJust . (`elemIndex` a226532_list)

f:= proc(n) local F,Fp,V,m,j,r;
  F:= ifactors(n)[2];
  Fp:= map(numtheory:-pi, F[..,1]);
  m:= max(Fp);
  V:= Vector(m);
  for j from 1 to nops(F) do V[Fp[j]]:= F[j,2] od:
  r:= ithprime(m)^V[m];
  for j from m-1 to 1 by -1 do r:= r * ithprime(j)^Bits:-Xor(V[j],V[j+1]) od;
  r
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Aug 21 2025

If k = Prod_{i=1..m} prime(i)^e(i), then a(k) = prime(m)^e(m) * Prod_{i=1..m-1} prime(i)^(e(i) xor e(i+1)). - Robert Israel, Aug 21 2025

A227987 If the run lengths of the binary representation of n are [1+r_1, 1+r_2, 1+r_3, ..., 1+r_k], then those of a(n) are [1+(r_1), 1+(r_1 XOR r_2), 1+(r_1 XOR r_2 XOR r_3), ..., 1+(r_1 XOR ... XOR r_k)], where XOR denotes the XOR binary operator.

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 7, 8, 19, 10, 11, 6, 51, 56, 15, 16, 71, 76, 9, 20, 21, 44, 23, 48, 13, 204, 25, 112, 455, 240, 31, 32, 271, 568, 143, 38, 307, 18, 79, 40, 83, 42, 43, 22, 179, 184, 47, 24, 783, 26, 27, 102, 819, 50, 207, 14, 1807, 3640, 911, 120, 3855

Offset: 1

Paul Tek, Aug 02 2013

This is a permutation of the natural numbers with inverse permutation A225607.
The sequence (n, a(n), a(a(n)), a(a(a(n))),...) is periodic for any n.
The run lengths of the binary representation of a fixed point are of the form [1, 1,...,1, K] (any number of ones followed by any number).

			For n=927:
(1) binary representation of n = "1110011111",
(2) run lengths of n = [1+2,1+1,1+4],
(3) run lengths of a(n) = [1+(2),1+(2 XOR 1),1+(2 XOR 1 XOR 4)]=[3,4,8],
(4) binary representation of a(n) = "111000011111111",
(5) a(n) = 28927.

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, Perl program for this sequence
Index entries for sequences that are permutations of the natural numbers

Cf. A056539, A226532, A225607 (inverse).

Perl
```
# See Tek link.
```

cp's OEIS Frontend

A226569 Inverse permutation to A226532.

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