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A076311
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floor(n/10) - 5*(n mod 10).
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7
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0, -5, -10, -15, -20, -25, -30, -35, -40, -45, 1, -4, -9, -14, -19, -24, -29, -34, -39, -44, 2, -3, -8, -13, -18, -23, -28, -33, -38, -43, 3, -2, -7, -12, -17, -22, -27, -32, -37, -42, 4, -1, -6, -11, -16, -21, -26, -31, -36, -41, 5, 0, -5, -10, -15, -20, -25, -30, -35
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| (n==0 modulo 17) iff (a(n)==0 modulo 17); 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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FORMULA
| a(n)= +a(n-1) +a(n-10) -a(n-11). G.f. x *(-5-5*x-5*x^2-5*x^3-5*x^4-5*x^5-5*x^6-5*x^7-5*x^8+46*x^9) / ( (1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) *(x-1)^2 ). - R. J. Mathar, Feb 20 2011
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EXAMPLE
| 12808 is not a multiple of 17, as 12808 -> 1280-5*8=1240 -> 124-5*0=124 -> 12-5*4=-8=17*(-1)+9, therefore the answer is NO;
is 9248 divisible by 17? 9248 -> 924-5*8=884 -> 88-5*4=68=17*4, therefore the answer is YES.
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CROSSREFS
| Cf. A008599, A076309, A076310, A076312.
Sequence in context: A178891 A044890 A007845 * A063284 A092454 A008706
Adjacent sequences: A076308 A076309 A076310 * A076312 A076313 A076314
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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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