A065652 a(0) = 0 and a(n+1) = if a(n) - 1 is new and > 0 then a(n) - 1 else a(n)*a(n) + 1 for n >= 0.

0, 1, 2, 5, 4, 3, 10, 9, 8, 7, 6, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97

Offset: 0

Author

Reinhard Zumkeller, Nov 10 2001

Keywords

• nonn

Comments

a(a(n)) = n: a self-inverse permutation of the natural numbers. a(x) = x iff x = A065654(k) for some k.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A065653, A065654.

Programs

Mathematica

a[n_] := a[n] = If[a[n - 1] > 1 && FreeQ[Array[a, n, 0], a[n - 1] - 1], a[n - 1] - 1, a[n - 1]^2 + 1]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Mar 19 2025 *)

Formula

a(A065653(k) + j) = A065653(k+1) - 1 - j for k >= 0 and 0 <= j < A065653(k+1) - A065653(k).