A115318 Inverse of A115316.

1, 2, 5, 3, 8, 4, 11, 6, 7, 9, 14, 10, 17, 12, 13, 15, 20, 16, 23, 18, 19, 21, 26, 22, 24, 25, 27, 28, 29, 30, 32, 31, 33, 34, 36, 37, 35, 39, 40, 42, 38, 43, 41, 45, 46, 48, 44, 49, 51, 52, 54, 55, 47, 57, 58, 60, 61, 63, 50, 64, 53, 66, 67, 69, 70, 72, 56, 73, 75, 76, 59, 78

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2006

Keywords

• nonn

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A115316, A115319.

Programs

Mathematica

nmax = 72;
nn = nmax + 10; (* estimated length of A115316 - should be increased in case of message "NotFound" in the output *)
np = Ceiling[nn/3] + 1;
nc = Ceiling[(2/3) nn];
pp = Prime[Range[np]];
cc = Partition[Select[Range[FindRoot[n == nc + PrimePi[n] + 1, {n, nc, 2nc}][[1, 2]] // Floor], CompositeQ], 2];
A115316 = Join[{1}, Riffle[pp, cc] // Flatten][[1 ;; nn]];
a[n_] := FirstPosition[A115316, n][[1]];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Nov 15 2021 *)

Formula

a(a(n)) = A115319(n).

a(n) = A115316(A115319(n)) = A115319(A115316(n)).