A065577 Number of Goldbach partitions of 10^n.

2, 6, 28, 127, 810, 5402, 38807, 291400, 2274205, 18200488, 149091160, 1243722370, 10533150855, 90350630388

Offset: 1

Author

Robert G. Wilson v, Dec 01 2001

Keywords

• nonn
• more

Comments

Number of ways of writing 10^n as the sum of two odd primes, when the order does not matter.

Examples

			a(1)=2 because 10 = 3+7 = 5+5;
a(2)=6 because 100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53; ...
		

Links

• Ivars Peterson's MathTrek, Goldbach's Prime Pairs
• Science News Online, Goldbach's Prime Pairs, week of Aug. 19, 2000; Vol. 158, No. 8.

Crossrefs

Cf. A001031, A073610, A107318.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{c = 0, lmt = n/2, p = 3}, While[p <= lmt, If[ PrimeQ[n - p], c++ ]; p = NextPrim@p]; c]; Array[f, 10] (* Robert G. Wilson v, Nov 01 2006 *)
a[n]:=Length[Select[n - Prime[Range[PrimePi[n/2]]], PrimeQ]]; Table[a[n],{n, 10^3, 10^3}] (* Luciano Ancora, Mar 16 2015 *)

Formula

a(n) = A061358(10^n).

Extensions

a(9) from Zak Seidov Nov 01 2006

a(10) from R. J. Mathar and David W. Wilson, Nov 02 2006

a(11) from David W. Wilson and Russ Cox, Nov 03 2006

a(12) from Russ Cox, Nov 04 2006

a(13) from Donovan Johnson, Nov 16 2009

a(14) from Huang Yuanbing (bailuzhou(AT)163.com), Dec 24 2009