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Search: id:A106444
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| 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, 128, 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This map from the multiplicative domain of N to that of GF(2)[X] preserves 'superfactorized' structures, e.g. A106490(n) = A106493(a(n)), A106491(n) = A106494(a(n)), A064372(n) = A106495(a(n)). Shares with A091202 and A106442 the property that maps A000040(n) to A014580(n). Differs from A091202 for the first time at n=32, where A091202(32)=32, while a(32)=128. Differs from A106442 for the first time at n=48, where A106442(48)=192, while a(48)=48. Differs from A106446 for the first time at n=11, where A106446(11)=25, while a(11)=13.
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LINKS
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A. Karttunen, Scheme-program for computing this sequence.
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(0)=0, a(1)=1, a(p_i) = A014580(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.
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EXAMPLE
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a(5) = 7, as 5 is the 3rd prime and the third irreducible GF(2)[X] polynomial x^2+x+1 is encoded as A014580(3) = 7. a(32) = a(2^5) = A048723(A014580(1),a(5)) = A048723(2,7) = 128. a(48) = a(3 * 2^4) = 3 X A048723(2,a(4)) = 3 X A048723(2,4) = 3 X 16 = 48.
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CROSSREFS
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Inverse: A106445.
Sequence in context: A130685 A125595 A091202 this_sequence A106442 A091204 A106446
Adjacent sequences: A106441 A106442 A106443 this_sequence A106445 A106446 A106447
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), May 09 2005
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