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A051034
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Minimal number of primes needed to sum to n.
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10
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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LINKS
| T. D. Noe, Table of n, a(n) for n=2..10000
Yannick Saouter, Vinogradov's theorem is true up to 10^20
Eric Weisstein's World of Mathematics, Prime Partition
Index entries for sequences related to Goldbach conjecture
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FORMULA
| 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
a(n) <= 3 for all n, assuming the Goldbach conjecture. - N. J. A. Sloane (njas(AT)research.att.com), Jan 20 2007
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EXAMPLE
| a(2) = 1 because 2 is already prime.
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.
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.
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PROG
| (PARI) issum(n, k)=if(k==1, isprime(n), k--; forprime(p=2, n, if(issum(n-p, k), return(1))); 0)
a(n)=my(k); while(!issum(n, k++), ); k \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| Cf. A025583, A004526, A000607, A051034, A051036, A010051, A061358, A068307, A103765.
Different from A072491.
Sequence in context: A183025 A072410 A072491 * A082477 A036430 A163377
Adjacent sequences: A051031 A051032 A051033 * A051035 A051036 A051037
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KEYWORD
| nonn,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Mar 16 2001
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