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1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, 1, 3, 2, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This sequence can be employed in a test for divisibility by seven. Given the decimal expansion of some natural number, it is easily shown that the following sum has the same remainder under division by seven as the original number and that this sum is stricly smaller than the original number: Successively take the digits of the number in reverse order and multiply each of them by the respective term of the sequence A033940, then sum the products. By repeating this process, since the sums decrease in size, one ends up with seven if and only if the initial number is divisible by seven. Example: 43638 is divisible by seven since 8*1 + 3*3 + 6*2 + 3*6 + 4*4 = 63 and 3*1 + 6*3 = 21 and 1*1 + 2*3 = 7. - Peter C. Heinig (algorithms(AT)gmx.de), Apr 16 2007
Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Feb 15 2009: Representation of (3^n) in the circle with seven equidistant points, (10^n) mod 7=(3^n) mod 7,
Representation of multiples of 3 in the circle (with seven equidistant points), see the Chryzodes links. - Eric Desbiaux (moongerms(AT)wanadoo.fr), Feb 14 2009
Equivalently 3^n mod 7. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2009]
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 24 2010: (Start)
Continued fraction expansion of (269+11*sqrt(1086))/490.
Decimal expansion of 1195/9009. (End)
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LINKS
| Author?, Chryzodes "3in7"
Author?, Chryzodes
Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).
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FORMULA
| a(n) = 10^n mod 7 = 3^n mod 7.
a(n)=a(n-1)-a(n-3)+a(n-4) = a(n-6). G.f.: (1+2x-x^2+5^x3)/((1-x)(1+x)(1-x+x^2)). a(n)=7/2 -7*(-1)^n/6 -4*A010892(n)/3-A010892(n-1)/3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2009]
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MATHEMATICA
| Table[PowerMod[10, n, 7], {n, 0, 200}] (* From Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
| (Other) 1.)sage: [power_mod(10, n, 7)for n in xrange(0, 106)] # 2.)sage: [power_mod(3, n, 7)for n in xrange(0, 106)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2009]
(MAGMA) [ 3^n mod 7: n in [0..75]]; // From Vincenzo Librandi, Feb 05 2011
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CROSSREFS
| Cf. A178247. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 24 2010]
Sequence in context: A057050 A123042 A121647 * A196047 A106409 A115510
Adjacent sequences: A033937 A033938 A033939 * A033941 A033942 A033943
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KEYWORD
| nonn,easy
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AUTHOR
| Jeff Burch (gburch(AT)erols.com)
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