id:A091204 - OEIS Search Results

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Deep multiplicative isomorphism from integers to GF(2)[X]-polynomials.

+0
6

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, 32, 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 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`This isomorphism can be used in most cases where mere A091202 would work, but in addition this preserves also the structures where we recurse on prime's index. E.g. we have: A091230(n) = a(A007097(n)) and A061775(n) = A091238(a(n)). This is possible because the permutation contains an image of itself in its restriction to primes, i.e. a(n) = A091227(a(A000040(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(a(i)) for primes 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: A091205.` `Sequence in context: A091202 A106444 A106442 this_sequence A106446 A036467 A006875` `Adjacent sequences: A091201 A091202 A091203 this_sequence A091205 A091206 A091207`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004`

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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.

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