Search: id:A045917
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%I A045917
%S A045917 0,1,1,1,2,1,2,2,2,2,3,3,3,2,3,2,4,4,2,3,4,3,4,5,4,3,5,3,4,6,3,5,6,2,5,
%T A045917 6,5,5,7,4,5,8,5,4,9,4,5,7,3,6,8,5,6,8,6,7,10,6,6,12,4,5,10,3,7,9,6,5,
%U A045917 8,7,8,11,6,5,12,4,8,11,5,8,10,5,6,13,9,6,11,7,7,14,6,8,13,5,8,11,7,9
%N A045917 From Goldbach problem: number of decompositions of 2n into unordered 
               sums of two primes.
%C A045917 Note that A002375 (which differs only at the n=2 term) is the main entry 
               for this sequence.
%D A045917 Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers,
               " Perseus Books, Cambridge, MA, 1996, Chapter 12, Pages 236-257.
%D A045917 H. Halberstam and H. E. Richert, 1974, "Sieve methods", Academic press, 
               London, New York, San Francisco.
%H A045917 H. J. Smith, <a href="b045917.txt">Table of n, a(n) for n = 1..20000</
               a>
%H A045917 M. Herkommer, <a href="http://www.petrospec-technologies.com/Herkommer/
               goldbach.htm">Goldbach Conjecture Research</a>
%H A045917 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GoldbachPartition.html">Goldbach Partition</a>
%H A045917 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">
               Goldbach's conjecture</a>
%H A045917 G. Xiao, WIMS server, <a href="http://wims.unice.fr/~wims/en_tool~number~goldbach.en.html">
               Goldbach</a>
%H A045917 <a href="Sindx_Go.html#Goldbach">Index entries for sequences related 
               to Goldbach conjecture</a>
%F A045917 From Halberstam and Richert : a(n)<(8+0(1))*c(n)*n/ln(n)^2 where c(n)=prod(p>
               2,(1-1/(p-1)^2))*prod(p|n,p>2,(p-1)/(p-2)). It is conjectured that 
               the factor 8 can be replaced by 2. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 16 2002
%t A045917 f[n_] := Length[Select[2n - Prime[Range[PrimePi[n]]], PrimeQ]]; Table[ 
               f[n], {n, 100}] (Paul Abbott, Jan 11 2005)
%Y A045917 A002375 (which differs only at the n=2 term) is the main entry for this 
               sequence.
%Y A045917 A023036 is the first appearance of n and A000954 is the last (assumed) 
               appearance of n.
%Y A045917 Sequence in context: A053597 A094570 A002375 this_sequence A029379 A058776 
               A029228
%Y A045917 Adjacent sequences: A045914 A045915 A045916 this_sequence A045918 A045919 
               A045920
%K A045917 nice,nonn,easy
%O A045917 1,5
%A A045917 Felice Russo (felice.russo(AT)katamail.com)

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