A002126 Number of solutions to n=p+q where p and q are primes or zero. (Formerly M0202 N0075)

1, 0, 2, 2, 1, 4, 1, 4, 2, 2, 3, 2, 2, 4, 3, 2, 4, 2, 4, 4, 4, 2, 5, 2, 6, 2, 5, 0, 4, 2, 6, 4, 4, 2, 7, 0, 8, 2, 3, 2, 6, 2, 8, 4, 6, 2, 7, 2, 10, 2, 8, 0, 6, 2, 10, 2, 6, 0, 7, 2, 12, 4, 5, 2, 10, 0, 12, 2, 4, 2, 10, 2, 12, 4, 9, 2, 10, 0, 14, 2, 8, 2, 9, 2, 16, 2, 9, 0, 8, 2, 18, 2, 8, 0, 9, 0, 14

Offset

0,3

Comments

Arises in studying the Goldbach conjecture.

References

P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. [Coll. Papers, Vol. II, pp. 354-382] [The sequence N_{n,2}]

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380.

Formula

G.f.: (1 + Sum_i x^prime(i))^2. [Corrected by T. D. Noe, Dec 05 2006]

Prog

(PARI) (a(n) = sum(k=0, n, zp(k)*zp(n-k))); {zp(n) = if( n==0, 1, isprime(n))}; /* Michael Somos, Jul 26 1999 */

Crossrefs

Cf. A002375, A045917, A061358, A073610

Sequence in context: A090002 A061298 A276468 * A350815 A129721 A268193

Adjacent sequences: A002123 A002124 A002125 * A002127 A002128 A002129

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(54) corrected by Paul Zimmermann, Mar 15 1996

Better description from Michael Somos, Jul 26 1999

Status

approved