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A115313
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a(n) = gcd(Lucas(n)+1, Fibonacci(n)+1).
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3
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2, 2, 1, 4, 6, 1, 2, 2, 7, 4, 10, 1, 18, 2, 13, 4, 94, 1, 34, 2, 123, 4, 178, 1, 322, 2, 233, 4, 1686, 1, 610, 2, 2207, 4, 3194, 1, 5778, 2, 4181, 4, 30254, 1, 10946, 2, 39603, 4, 57314, 1, 103682, 2, 75025, 4, 542886, 1, 196418, 2, 710647, 4, 1028458, 1
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OFFSET
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1,1
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COMMENTS
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Here Lucas is: Lucas(1)=1, Lucas(2)=3 and, for n>2, Lucas(n) = Lucas(n-1)+Lucas(n-2). See A000032.
a(n) is prime for n = 1, 2, 7, 8, 9, 14, 15, 20, 26, 27, 32, 33, 38, 44, 50, 56, 62, 68, 74, 80, 86, 87, ... - Vincenzo Librandi, Dec 24 2015
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LINKS
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EXAMPLE
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a(15) = 13 since F(15) + 1 = 13*47 and L(15) + 1 = 3*5*7*13.
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MATHEMATICA
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lucas[1]=1; lucas[2]=3; lucas[n_]:= lucas[n]= lucas[n-1] + lucas[n-2]; Table[GCD[lucas[i]+1, Fibonacci[i]+1], {i, 60}]
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PROG
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(Magma) [Gcd(Lucas(n)+1, Fibonacci(n)+1): n in [1..60]]; // Vincenzo Librandi, Dec 24 2015
(PARI) a(n) = gcd(fibonacci(n+1)+fibonacci(n-1)+1, fibonacci(n)+1); \\ Altug Alkan, Dec 24 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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