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A215501
Inverse of permutation in A215366.
3
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).
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
KEYWORD
nonn,look
AUTHOR
Alois P. Heinz, Aug 13 2012
STATUS
approved