A366264 Inverse of A366263, where A366263 is the Doudna sequence permuted by Blue code.

0, 1, 3, 2, 5, 4, 15, 7, 6, 14, 17, 13, 51, 16, 12, 8, 85, 11, 255, 19, 18, 50, 257, 22, 10, 84, 9, 49, 771, 21, 1285, 25, 48, 254, 20, 28, 3855, 256, 86, 52, 4369, 55, 13107, 87, 23, 770, 21845, 59, 30, 31, 252, 253, 65535, 26, 54, 82, 258, 1284, 65537, 62, 196611, 3854, 53, 42, 80, 81, 327685, 259, 768, 61, 983055

Offset: 1

Author

Antti Karttunen, Oct 06 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A156552, A193231, A366263 (inverse map).

Cf. A055396, A268389.

Programs

PARI

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) };
A366264(n) = A193231(A156552(n));

Formula

a(n) = A193231(A156552(n)).

For all n >= 0, a(A366263(n)) = n, and for all n >= 1, A366263(a(n)) = n.

For all n >= 2, 1+A268389(a(n)) = A055396(n).