2,3

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, Link to a section of The World of Mathematics.

Index entries for sequences related to Goldbach conjecture

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

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.

Cf. A004526, A000607, A051034, A051036, A010051, A061358, A068307, A103765.

Different from A072491.

Sequence in context: A071854 A072410 A072491 this_sequence A082477 A036430 A163377

Adjacent sequences: A051031 A051032 A051033 this_sequence A051035 A051036 A051037

nonn,nice,easy

Eric Weisstein (eric(AT)weisstein.com)

More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Mar 16 2001