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Search: id:A155751
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| A155751 |
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A variation on 10^n mod 17 |
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+0
1
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| 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence can be employed in a test for divisibility by 17 and works like A033940 works for 7.
The use of negative coefficients ensures the termination of the test because the modulus of the intermediate sum at each step of the test decreases stricly.
The test is successful if the final sum is 0.
The negative coefficients have the form (10^n mod 17) - 17 when 10^n mod 17 > 8.
Example: 9996 is divisible by 17 since |6*1 + 9*(-7) + 9*(-2) + 9*(-3)| = 102 and 2*1 + 0*(-7) + 1*(-2) = 0.
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FORMULA
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a(n)= -a(n-8). G.f.:(1-7x-2x^2-3x^3+4x^4+6x^5-8x^6+5x^7)/(1+x^8). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2009]
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CROSSREFS
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Cf. A033940, A119910, A117378.
Sequence in context: A021857 A163333 A116369 this_sequence A092234 A160101 A065476
Adjacent sequences: A155748 A155749 A155750 this_sequence A155752 A155753 A155754
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KEYWORD
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easy,sign,uned
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AUTHOR
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Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009, Feb 08 2009
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EXTENSIONS
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How is the sequence defined? - N. J. A. Sloane (njas(AT)research.att.com), Feb 08 2009
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