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Search: id:A071970
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| A071970 |
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List the positive rationals in the order in which they are produced by the Stern sequence A002487 and apply the Sagher map to turn them into integers. |
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3
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| 1, 2, 4, 3, 18, 12, 9, 8, 48, 45, 50, 20, 75, 72, 16, 5, 200, 112, 147, 288, 320, 175, 98, 28, 245, 800, 192, 63, 392, 80, 25, 6, 180, 675, 648, 176, 847, 490, 300, 99, 3872, 832, 845, 600, 1008, 1323, 162, 108, 567, 1176, 720, 325, 5408, 704, 363, 90, 700, 539
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The Sagher map sends Product p_i^e_i / Product q_i^f_i (p_i and q_i being distinct primes) to Product p_i^(2e_i) * Product q_i^(2f_i-1). This is multiplicative.
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REFERENCES
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Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823.
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EXAMPLE
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The first few rationals and their images are 1/1 -> 1, 1/2 -> 2, 2/1 -> 4, 1/3 -> 3, 3/2 -> 18, 2/3 -> 12, 3/1 -> 9, 1/4 -> 8, ...
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PROGRAM
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(PARI) s(n)=if(n<2, n>0, if(n%2, s((n+1)/2)+s((n-1)/2), s(n/2))) /* A002487(n) */
(PARI) a(n)=local(v); if(n, v=factor(s(n)/s(n+1))~; prod(k=1, length(v), v[1, k]^if(v[2, k]<0, -1-2*v[2, k], 2*v[2, k])), 0)
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CROSSREFS
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Cf. A002487, A060837.
Sequence in context: A109429 A114894 A053124 this_sequence A111172 A009116 A118434
Adjacent sequences: A071967 A071968 A071969 this_sequence A071971 A071972 A071973
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas, Jun 19 2002
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EXTENSIONS
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More terms from Michael Somos, Jul 19 2002
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