A106446 Doubly-recursed cross-domain bijection from N to GF(2)[X]. Variant of A091204 and A106444.

0, 1, 2, 3, 4, 7, 6, 11, 8, 5, 14, 25, 12, 19, 22, 9, 16, 47, 10, 31, 28, 29, 50, 13, 24, 21, 38, 15, 44, 61, 18, 137, 128, 43, 94, 49, 20, 55, 62, 53, 56, 97, 58, 115, 100, 27, 26, 37, 48, 69, 42, 113, 76, 73, 30, 79, 88, 33, 122, 319, 36, 41, 274, 39, 64, 121, 86, 185

Offset

0,3

Comments

Differs from A091204 for the first time at n=32, where A091204(32)=32, while a(32)=128. Differs from A106444 for the first time at n=11, where A106444(11)=13, while a(11)=25.

Links

Table of n, a(n) for n=0..67.

A. Karttunen, Scheme-program for computing this sequence.

Index entries for sequences that are permutations of the natural numbers

Formula

a(0)=0, a(1)=1, a(p_i) = A014580(a(i)) for primes p_i with index i and for composites n = p_i^e_i * p_j^e_j * p_k^e_k * ..., a(n) = A048723(a(p_i), a(e_i)) X A048723(a(p_j), a(e_j)) X A048723(a(p_k), a(e_k)) X ..., where X stands for carryless multiplication of GF(2)[X] polynomials (A048720) and A048723(n, y) raises the n-th GF(2)[X] polynomial to the y:th power.

Example

a(5) = 7, as 5 is the 3rd prime, a(3)=3 and the third irreducible GF(2)[X] polynomial x^2+x+1 is encoded as A014580(3) = 7. a(11) = 25, as 11 is the 5th prime, a(5)=7 and the seventh irreducible GF(2)[X] polynomial x^4+x^3+1 is encoded as A014580(7) = 25. a(32) = a(2^5) = A048723(a(2),a(5)) = A048723(2,7) = 128.

Crossrefs

Inverse: A106447. Variant: A091204.

Sequence in context: A106444 A106442 A091204 * A321220 A036467 A006875

Adjacent sequences: A106443 A106444 A106445 * A106447 A106448 A106449

Keyword

nonn

Author

Antti Karttunen, May 09 2005

Status

approved