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A076309
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floor(n/10) - 2*(n mod 10).
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7
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0, -2, -4, -6, -8, -10, -12, -14, -16, -18, 1, -1, -3, -5, -7, -9, -11, -13, -15, -17, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, 5, 3, 1, -1, -3, -5, -7, -9, -11, -13, 6, 4, 2, 0, -2, -4, -6, -8, -10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| (n==0 modulo 7) iff (a(n)==0 modulo 7); applied recursivly, this property provides a divisibility test for numbers given in base 10 notation.
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REFERENCES
| Karl Menninger, Rechenkniffe, Vandenhoeck & Ruprecht in Goettingen (1961), 79A.
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LINKS
| Eric Weisstein's World of Mathematics, Divisibility Tests.
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FORMULA
| a(n)= +a(n-1) +a(n-10) -a(n-11).
G.f.: x*(-2-2*x-2*x^2-2*x^3-2*x^4-2*x^5-2*x^6-2*x^7-2*x^8+19*x^9)/ ((1+x) * (x^4-x^3+x^2-x+1) * (x^4+x^3+x^2+x+1) * (x-1)^2).
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EXAMPLE
| 695591 is not a multiple of 7, as 695591 -> 69559-2*1=69557 -> 6955-2*7=6941 -> 694-2*1=692 -> 69-2*2=65=7*9+2, therefore the answer is No; is 3206 divisible by 7? 3206 -> 320-2*6=308 -> 30-2*8=14=7*2, therefore the answer is Yes, indeed 3206=2*7*229.
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CROSSREFS
| Cf. A008589, A076310, A076311, A076312.
Sequence in context: A088116 A100817 A074157 * A088133 A115299 A076312
Adjacent sequences: A076306 A076307 A076308 * A076310 A076311 A076312
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KEYWORD
| sign
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 06 2002
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