A190681 Number of partitions of 10^n into 2 composite relatively prime parts.

0, 0, 2, 61, 899, 11219, 126905, 1374229, 14529946, 151426672, 1563147978, 16031036348

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Example

a(2)=2 because 10^2 = 9 + 91 = 49 + 51, 9 and 91 are composite and coprime, 49 and 51 are composite and coprime.

Mathematica

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]

Prog

(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

Crossrefs

Cf. A000041, A023022, A000837.

Sequence in context: A299224 A037065 A065589 * A181005 A289644 A347606

Adjacent sequences: A190678 A190679 A190680 * A190682 A190683 A190684

Keyword

nonn

Author

Zak Seidov, May 17 2011

Extensions

a(9)-a(10) from Charles R Greathouse IV, May 18 2011

a(11) from Charles R Greathouse IV, May 20 2011

Status

approved