A002122 a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t). (Formerly M0273 N0096)

1, 0, -2, 2, 3, -4, -1, 8, -1, -10, 9, 16, -18, -12, 42, 4, -58, 40, 82, -88, -54, 188, 18, -248, 151, 354, -338, -260, 760, 120, -1031, 574, 1460, -1324, -1076, 2948, 542, -3962, 2075, 5644, -4868, -4290, 11035, 2418, -14900, 7346, 21300, -17652, -16323, 40442, 9768, -54476, 25675, 78290, -62456

Offset

0,3

Comments

Arises in studying the Goldbach conjecture.

The last negative term appears to be a(485). - T. D. Noe, Dec 05 2006

References

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..1000

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. [The sequence G_n]

Index entries for sequences related to Goldbach conjecture

Formula

G.f.: 1/(1+Sum_{k>0} (-x)^prime(k))^2.

Prog

(Haskell)
a002122 n = a002122_list !! n
a002122_list = uncurry conv $ splitAt 1 a002121_list where
   conv xs (z:zs) = sum (zipWith (*) xs $ reverse xs) : conv (z:xs) zs
-- Reinhard Zumkeller, Mar 21 2014

Crossrefs

Cf. A002121.

Sequence in context: A008951 A119473 A336889 * A105689 A351080 A187200

Adjacent sequences: A002119 A002120 A002121 * A002123 A002124 A002125

Keyword

sign

Author

N. J. A. Sloane

Extensions

Edited by Vladeta Jovovic, Mar 29 2003

Entry revised by N. J. A. Sloane, Dec 04 2006

Status

approved