%I A051034
%S A051034 1,1,2,1,2,1,2,2,2,1,2,1,2,2,2,1,2,1,2,2,2,1,2,2,2,3,2,1,2,1,2,2,2,3,
%T A051034 2,1,2,2,2,1,2,1,2,2,2,1,2,2,2,3,2,1,2,2,2,3,2,1,2,1,2,2,2,3,2,1,2,2,2,
               1,2,1,2,2,2,3,2,1,2,2,2,1,2,2,
%U A051034 2,3,2,1,2,2,2,3,2,3,2,1,2,2,2,1,2,1,2,2,2,1,2,1,2,2,2
%N A051034 Minimal number of primes needed to sum to n.
%H A051034 T. D. Noe, <a href="b051034.txt">Table of n, a(n) for n=2..10000</a>
%H A051034 Yannick Saouter, <a href="http://citeseer.ist.psu.edu/cache/papers/cs/
               16643/ftp:zSzzSzftp.irisa.frzSztechreportszSz1995zSzPI-977.pdf/vinogradov-s-theorem-is.pdf">
               Vinogradov's theorem is true up to 10^20</a>
%H A051034 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimePartition.html">Link to a section of The World of Mathematics.</
               a>
%H A051034 <a href="Sindx_Go.html#Goldbach">Index entries for sequences related 
               to Goldbach conjecture</a>
%F A051034 a(n) = 1 iff n is prime. a(2n) = 2 (for n > 1) if Goldbachs's conjecture 
               is true. a(2n+1) = 2 (for n >= 1) if 2n+1 is not prime, but 2n-1 
               is. a(2n+1) >= 3 (for n >= 1) if both 2n+1 and 2n-1 are not primes 
               (for sufficiently large n, a(2n+1) = 3 by Vinogradov's theorem, 1937). 
               - Franz Vrabec (franz.vrabec(AT)aon.at), Nov 30 2004
%F A051034 a(n) <= 3 for all n, assuming the Goldbach conjecture. - N. J. A. Sloane 
               (njas(AT)research.att.com), Jan 20 2007
%e A051034 a(2) = 1 because 2 is already prime.
%e A051034 a(4) = 2 because 4 = 2+2 is a partition of 4 into 2 prime parts and there 
               is no such partition with fewer terms.
%e A051034 a(27) = 3 because 27 = 3+5+19 is a partition of 27 into 3 prime parts 
               and there is no such partition with fewer terms.
%Y A051034 Cf. A004526, A000607, A051034, A051036, A010051, A061358, A068307, A103765.
%Y A051034 Different from A072491.
%Y A051034 Sequence in context: A071854 A072410 A072491 this_sequence A082477 A036430 
               A163377
%Y A051034 Adjacent sequences: A051031 A051032 A051033 this_sequence A051035 A051036 
               A051037
%K A051034 nonn,nice,easy
%O A051034 2,3
%A A051034 Eric Weisstein (eric(AT)weisstein.com)
%E A051034 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Mar 16 
               2001