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A065577
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Number of Goldbach partitions of 10^n.
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9
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2, 6, 28, 127, 810, 5402, 38807, 291400, 2274205, 18200488, 149091160, 1243722370, 10533150855, 90350630388
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OFFSET
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1,1
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COMMENTS
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Number of ways of writing 10^n as the sum of two odd primes, when the order does not matter.
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LINKS
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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.
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FORMULA
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a(n) = A061358(10^n).
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EXAMPLE
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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; ...
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A001031.
Cf. A073610, A107318.
Sequence in context: A189238 A226497 A307523 * A227294 A302336 A225877
Adjacent sequences: A065574 A065575 A065576 * A065578 A065579 A065580
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Dec 01 2001
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EXTENSIONS
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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
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STATUS
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approved
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