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A190681
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Number of partitions of 10^n into 2 composite relatively prime parts.
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0
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0, 0, 2, 61, 899, 11219, 126905, 1374229, 14529946, 151426672, 1563147978, 16031036348
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(2)=2 because 10^2 = 9 + 91 = 49 + 51, 9 and 91 are composite and coprime, 49 and 51 are composite and coprime.
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MATHEMATICA
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a[n_] := Module[{cnt=0}, Do[If[!PrimeQ[k]&&!PrimeQ[10^n-k]&&GCD[k, 10^n-k]==1, cnt++], {k, 3, (1/2)10^n, 2}]; cnt]
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PROG
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(PARI) a(n) = my(N=10^n, s=0); forstep(k=9, N/2, [2, 2, 4, 2], s += !isprime(k) & !isprime(N-k)); s \\ Charles R Greathouse IV, May 17 2011
(PARI) a(n)=my(N=10^n, s=0, p=7); forprime(q=11, N/2, forstep(k=p+2, q-2, 2, s+=k%5&!isprime(N-k)); p=q); s+sum(k=precprime(N/2)+2, N/2, gcd(k, 10)==1&!isprime(N-k)) \\ Charles R Greathouse IV, May 17 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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