A091202 - OEIS

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A091202

Factorization-preserving isomorphism from integers to GF(2)[X]-polynomials.

0, 1, 2, 3, 4, 7, 6, 11, 8, 5, 14, 13, 12, 19, 22, 9, 16, 25, 10, 31, 28, 29, 26, 37, 24, 21, 38, 15, 44, 41, 18, 47, 32, 23, 50, 49, 20, 55, 62, 53, 56, 59, 58, 61, 52, 27, 74, 67, 48, 69, 42, 43, 76, 73, 30, 35, 88, 33, 82, 87, 36, 91, 94, 39, 64, 121, 46, 97, 100, 111, 98 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`E.g. we have the following identities: A000005(n) = A091220(a(n)), A001221(n) = A091221(a(n)), A001222(n) = A091222(a(n)), A008683(n) = A091219(a(n)), A014580(n) = a(A000040(n)), A049084(n) = A091227(a(n)).`
	LINKS	`A. Karttunen, Scheme-program for computing this sequence.` `Index entries for sequences operating on GF(2)[X]-polynomials` `Index entries for sequences that are permutations of the natural numbers`
	FORMULA	`a(0)=0, a(1)=1, a(p_i) = A014580(i) for primes p_i with index i and for composites a(p_i * p_j * ...) = a(p_i) X a(p_j) X ..., where X stands for carryless multiplication of GF(2)[X] polynomials (A048720).`
	CROSSREFS	`Inverse: A091203.` `Several "deep" variants exists: A091204, A106442, A106444, A106446.` `Sequence in context: A120225 A130685 A125595 * A106444 A106442 A091204` `Adjacent sequences: A091199 A091200 A091201 * A091203 A091204 A091205`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004`

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Last modified February 14 04:10 EST 2012. Contains 205570 sequences.