id:A091203 - OEIS Search Results

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

+0
12

0, 1, 2, 3, 4, 9, 6, 5, 8, 15, 18, 7, 12, 11, 10, 27, 16, 81, 30, 13, 36, 25, 14, 33, 24, 17, 22, 45, 20, 21, 54, 19, 32, 57, 162, 55, 60, 23, 26, 63, 72, 29, 50, 51, 28, 135, 66, 31, 48, 35, 34, 243, 44, 39, 90, 37, 40, 99, 42, 41, 108, 43, 38, 75, 64, 225, 114, 47, 324 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`E.g. we have the following identities: A000040(n) = a(A014580(n)), A091219(n) = A008683(a(n)), A091220(n) = A000005(a(n)), A091221(n) = A001221(a(n)), A091222(n) = A001222(a(n)), A091225(n) = A010051(a(n)), A091227(n) = A049084(a(n)), A091247(n) = A066247(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. For n's coding an irreducible polynomial ir_i, that is if n=A014580(i), we have a(n) = A000040(i) and for composite polynomials a(ir_i X ir_j X ...) = p_i * p_j * ..., where p_i = A000040(i) and X stands for carryless multiplication of GF(2)[X] polynomials (A048720) and * for the ordinary multiplication of integers (A004247).`
	CROSSREFS	`Inverse: A091202.` `Several "deep" variants exists: A091205, A106443, A106445, A106447.` `Sequence in context: A124418 A112480 A112095 this_sequence A106445 A106443 A091205` `Adjacent sequences: A091200 A091201 A091202 this_sequence A091204 A091205 A091206`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004`

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Last modified July 26 23:19 EDT 2008. Contains 142293 sequences.

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