A332450 Self-inverse permutation of natural numbers, "Blue code" conjugated by A156552 and its inverse: a(n) = A005940(1+A193231(A156552(n))).

1, 2, 4, 3, 6, 5, 16, 8, 9, 27, 14, 18, 100, 11, 25, 7, 210, 12, 256, 20, 21, 147, 38, 45, 15, 385, 10, 98, 1156, 30, 1938, 50, 121, 2187, 35, 125, 234256, 23, 315, 245, 6902, 72, 3496900, 120, 24, 1083, 9699690, 108, 81, 32, 15625, 1458, 65536, 75, 225, 231, 57, 2185, 106, 243, 8836, 771147, 150, 105, 143, 154, 14946, 68, 529, 162

Offset: 1

Author

Antti Karttunen, Feb 15 2020

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences related to polynomials in ring GF(2)[X]
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A005940, A156552, A193231, A332449, A332451, A366263.

Cf. A293448 (A057889 similarly conjugated).

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A156552(n) = {my(f = factor(n), 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) }; \\ From A193231
A332450(n) = A005940(1+A193231(A156552(n)));

Formula

a(n) = A005940(1+A193231(A156552(n))).

a(A003961(n)) = A332451(a(n)); a(A332451(n)) = A003961(a(n)).

a(n) = A366263(A156552(n)). - Antti Karttunen, Oct 06 2023