login
Inverse of permutation in A215366.
3

%I #23 Nov 14 2023 09:24:20

%S 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,

%T 24,25,98,26,140,19,33,47,34,27,196,69,48,28,273,35,374,36,37,99,509,

%U 29,49,38,70,50,685,39,51,40,100,141,916,41,1213,197,52,30

%N Inverse of permutation in A215366.

%C 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).

%H Alois P. Heinz, <a href="/A215501/b215501.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

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

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

%p g:= proc(n, i) option remember; `if`(n=0 or i<2, [2^n], [seq(

%p map(p->p*ithprime(i)^j, g(n-i*j, i-1))[], j=0..n/i)]) end:

%p b:= proc() local l, i; l:=[]; i:=0;

%p proc(n) while nops(l)<n do

%p l:=[l[], sort(g(i, i))[]]; i:=i+1 od; l[n]

%p end

%p end():

%p a:= proc() local t, a; t, a:= 0, proc() -1 end;

%p proc(n) local h;

%p while a(n) = -1 do

%p t:= t+1; h:= b(t);

%p if a(h) = -1 then a(h):= t fi

%p od; a(n)

%p end

%p end():

%p seq(a(n), n=1..100);

%t 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}]]];

%t b[n_] := Module[{l, i}, l = {}; i = 0; While[Length[l] < n, l = Join[l, Sort[g[i, i]]]; i++]; l[[n]]];

%t 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]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Nov 14 2023, after _Alois P. Heinz_ *)

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

%K nonn,look

%O 1,2

%A _Alois P. Heinz_, Aug 13 2012