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Search: id:A089128
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| A089128 |
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Greatest common divisor of n^2-6 and n^2+6. |
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+0
3
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| 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The second term of sequences of this type for n=0,1,2... form the sequence 1,2,1,2,1,...in decimal .1212121212... = 4/33
Multiplicative with a(p^e) = GCD(p^e, 6). David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
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FORMULA
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a(n) = GCD(6, n). David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
a(n) = 1 + [2|n] + 2*[3|n] + 2*[6|n] = (15 + 5*(-1)^n + 4*cos(n*Pi/3) + 12*cos(n*2*Pi/3))/6, where [x|y] is 1 if x divides y, 0 otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 15, 2005.
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PROGRAM
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(PARI) g(n) = for(x=0, n, print1(gcd(x^2-6, x^2+6)", "))
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CROSSREFS
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Sequence in context: A002950 A121090 A010135 this_sequence A106687 A083463 A013672
Adjacent sequences: A089125 A089126 A089127 this_sequence A089129 A089130 A089131
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 05 2003
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