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A073830
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a(n) = 4*((n-1)! + 1) + n (mod n*(n + 2)).
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5
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0, 2, 0, 8, 0, 10, 56, 12, 22, 14, 0, 16, 182, 18, 34, 20, 0, 22, 380, 24, 46, 26, 552, 28, 29, 30, 58, 32, 0, 34, 992, 36, 37, 38, 74, 40, 1406, 42, 82, 44, 0, 46, 1892, 48, 94, 50, 2256, 52, 53, 54, 106, 56, 2862, 58, 59, 60, 118, 62, 0, 64, 3782, 66, 67, 68, 134, 70
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OFFSET
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1,2
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LINKS
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FORMULA
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For n > 1: a(n) = 0 iff (n, n+2) are twin primes (Clement, 1949).
If p is an odd prime, and p+2 is composite, then a(p) = p*(p+1).
If m is composite, and m+2 is prime, then a(m) = 2*(m+2).
If n even >= 4, a(n) = n + 4.
If p prime >= 5, a(p^2) = p^2 + 4. (End)
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MAPLE
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4*((n-1)!+1)+n ;
modp(%, n*(n+2)) ;
end proc:
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MATHEMATICA
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PROG
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(Magma) [(4*(Factorial(n-1)+1)+n) mod (n^2+2*n): n in [1..70]]; // Vincenzo Librandi, May 04 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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