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 A002121 a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p). (Formerly M0023 N0005) 2
 1, 0, -1, 1, 1, -1, 0, 2, 0, -2, 2, 4, -3, -2, 8, 1, -8, 8, 12, -11, -4, 25, 4, -24, 21, 40, -31, -16, 82, 14, -81, 71, 131, -99, -48, 258, 46, -249, 223, 422, -303, -162, 825, 169, -791, 714, 1360, -955, -503, 2641, 573, -2479, 2263, 4365, -2941, -1592, 8436, 1978, -7830, 7212, 14083, -9133, -4992, 26970, 6688, -24590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Arises in studying the Goldbach conjecture. The last negative term appears to be a(303). - 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. FORMULA G.f.: 1/(1+Sum_{k>0} (-x)^prime(k)). - Vladeta Jovovic, Mar 29 2003 PROG (Haskell) import Data.List (genericIndex) a002121 n = genericIndex a002121_list n a002121_list = 1 : 0 : -1 : f 0 (-1) 3 where    f v w x = y : f w y (x + 1) where      y = sum (map (a002121 . (x -)) \$ takeWhile (<= x) a065091_list) - v -- Reinhard Zumkeller, Mar 21 2014 CROSSREFS Cf. A002100-A002125. Cf. A065091. Sequence in context: A308212 A181346 A300815 * A279158 A273166 A300822 Adjacent sequences:  A002118 A002119 A002120 * A002122 A002123 A002124 KEYWORD sign,easy,look AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Mar 29 2003 Entry revised by N. J. A. Sloane, Dec 04 2006 STATUS approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)