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Search: id:A065577
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| A065577 |
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Number of Goldbach partitions of 10^n. |
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+0
7
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| 2, 6, 28, 127, 810, 5402, 38807, 291400, 2274205, 18200488, 149091160, 1243722370
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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Ivars Peterson's MathTrek, Goldbach's Prime Pairs
Science News Online, week of Aug. 19, 2000; Vol. 158, No. 8 Goldbach's Prime Pairs
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FORMULA
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a(n)=A061358(10^n). Cf. A073610, A107318.
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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 *)
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CROSSREFS
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Cf. A001031.
Sequence in context: A115156 A089748 A047125 this_sequence A004984 A086633 A109570
Adjacent sequences: A065574 A065575 A065576 this_sequence 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 (rgwv(AT)rgwv.com), Dec 01 2001
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EXTENSIONS
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a(9) from Zak Seidov (zakseidov(AT)yahoo.com) 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
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