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A002122 a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).
(Formerly M0273 N0096)
1
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 (list; graph; refs; listen; history; text; internal format)
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

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 G_n]

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.

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: A087824 A008951 A119473 * A105689 A187200 A117632

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

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)