A065577 Number of Goldbach partitions of 10^n.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..14.

Ivars Peterson's MathTrek, Goldbach's Prime Pairs

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

Formula

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

Example

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; ...

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 *)

Crossrefs

Cf. A001031, A073610, A107318.

Sequence in context: A189238 A226497 A307523 * A227294 A302336 A225877

Adjacent sequences: A065574 A065575 A065576 * A065578 A065579 A065580

Keyword

nonn,more

Author

Robert G. Wilson v, Dec 01 2001

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

Status

approved