cp's OEIS Frontend

A065577 Number of Goldbach partitions of 10^n.

%I A065577 #26 Dec 17 2022 20:09:58
%S A065577 2,6,28,127,810,5402,38807,291400,2274205,18200488,149091160,
%T A065577 1243722370,10533150855,90350630388
%N A065577 Number of Goldbach partitions of 10^n.
%C A065577 Number of ways of writing 10^n as the sum of two odd primes, when the order does not matter.
%H A065577 Ivars Peterson's MathTrek, <a href="http://www.maa.org/mathland/mathtrek_8_21_00.html">Goldbach's Prime Pairs</a>
%H A065577 Science News Online, <a href="http://www.sciencenews.org/20000819/mathtrek.asp">Goldbach's Prime Pairs</a>, week of Aug. 19, 2000; Vol. 158, No. 8.
%F A065577 a(n) = A061358(10^n).
%e A065577 a(1)=2 because 10 = 3+7 = 5+5;
%e A065577 a(2)=6 because 100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53; ...
%t A065577 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 *)
%t A065577 a[n]:=Length[Select[n - Prime[Range[PrimePi[n/2]]], PrimeQ]]; Table[a[n],{n, 10^3, 10^3}] (* _Luciano Ancora_, Mar 16 2015 *)
%Y A065577 Cf. A001031, A073610, A107318.
%K A065577 nonn,more
%O A065577 1,1
%A A065577 _Robert G. Wilson v_, Dec 01 2001
%E A065577 a(9) from _Zak Seidov_ Nov 01 2006
%E A065577 a(10) from _R. J. Mathar_ and _David W. Wilson_, Nov 02 2006
%E A065577 a(11) from _David W. Wilson_ and _Russ Cox_, Nov 03 2006
%E A065577 a(12) from _Russ Cox_, Nov 04 2006
%E A065577 a(13) from _Donovan Johnson_, Nov 16 2009
%E A065577 a(14) from Huang Yuanbing (bailuzhou(AT)163.com), Dec 24 2009