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Search: id:A117966
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| A117966 |
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Balanced ternary enumeration of integers; write n in ternary, and then replace 2's with (-1)'s. |
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+0
4
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| 0, 1, -1, 3, 4, 2, -3, -2, -4, 9, 10, 8, 12, 13, 11, 6, 7, 5, -9, -8, -10, -6, -5, -7, -12, -11, -13, 27, 28, 26, 30, 31, 29, 24, 25, 23, 36, 37, 35, 39, 40, 38, 33, 34, 32, 18, 19, 17, 21, 22, 20, 15, 16, 14, -27, -26, -28, -24, -23, -25, -30, -29, -31, -18, -17, -19, -15, -14, -16, -21, -20, -22, -36
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A004488(n) = A117966^{-1}(-A117966(n)). I.e., if A117966(n) <= 0, A004488(n) = A117967(-A117966(n)), and if A117966(n) > 0, A004488(n) = A117968(A117966(n)).
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REFERENCES
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, pp. 173-175
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..729
Ken Levasseur, The Balanced Ternary Number System
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FORMULA
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a(0)=0, a(3n)=3a(n), a(3n+1)=3a(n)+1, a(3n+2)=3a(n)-1. G.f. satisfies A(x) = 3A(x^3) + x - x^2.
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EXAMPLE
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7 in base 3 is 21; changing the 2 to a (-1) gives (-1)*3+1 = -2, so a(7) = -2.
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PROGRAM
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(MIT/GNU Scheme:) (define (A117966 n) (let loop ((z 0) (i 0) (n n)) (if (zero? n) z (loop (+ z (* (expt 3 i) (if (= 2 (modulo n 3)) -1 (modulo n 3)))) (1+ i) (floor->exact (/ n 3))))))
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CROSSREFS
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Cf. A117967, A117868, A001057, A004488.
Sequence in context: A143486 A021749 A088916 this_sequence A121891 A011414 A084511
Adjacent sequences: A117963 A117964 A117965 this_sequence A117967 A117968 A117969
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KEYWORD
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base,sign
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 05 2006
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EXTENSIONS
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 19 2008, added the table for n=0..729 and the Scheme function.
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