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Search: id:A097151
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| A097151 |
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Digits of balanced base-10 representations of nonnegative integers (least significant digits first). |
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+0
2
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| 0, 1, 2, 3, 4, -5, 1, -4, 1, -3, 1, -2, 1, -1, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, -5, 2, -4, 2, -3, 2, -2, 2, -1, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, -5, 3, -4, 3, -3, 3, -2, 3, -1, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, -5, 4, -4, 4, -3, 4, -2, 4, -1, 4, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, -5, -5, 1, -4, -5, 1, -3, -5, 1, -2, -5, 1, -1, -5, 1, 0, -5, 1, 1, -5, 1, 2, -5, 1, 3, -5, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Definition 9.1.2. of the Crandall-Pomerance book is: "The balanced base-B representation of a nonnegative integer x is the shortest sequence of integer digits (x_i) such that each digit satisfies -floor(B/2) <= x_i <= floor((B-1)/2) and x = sum(i=0,D-1,x_i*B^i)." (I have replaced floor and sigma symbols with "floor" and "sum" for inclusion here.) The D digits x_0, x_1, x_2, ..., x_(D-1) are included in this order in this sequence and in the opposite order in A097150.
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 408.
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EXAMPLE
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As the only digits permissible are in {-5,-4,-3,-2,-1,0,1,2,3,4},
5 = -5 + 1*10 is the first number requiring two of these digits: -5,1.
A097150 is the same sequence but with the digits in reverse order.
Also, 45 = -5 - 5*10 + 1*10^2 has digits -5,-5,1,
54 = 4 - 5*10 + 1*10^2 has digits 4,-5,1 and
55 = -5 - 4*10 + 1*10^2 has digits -5,-4,1.
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CROSSREFS
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Cf. A097150 (most significant digits first).
Sequence in context: A053827 A033926 A050269 this_sequence A071500 A071516 A026284
Adjacent sequences: A097148 A097149 A097150 this_sequence A097152 A097153 A097154
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KEYWORD
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base,easy,sign
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 27 2004
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