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).
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
Offset: 0
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
Programs
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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 -
Mathematica
CoefficientList[Series[1/(1+Sum[(-x)^Prime[k],{k,20}]),{x,0,70}],x] (* Harvey P. Dale, Aug 26 2020 *)
Formula
G.f.: 1/(1+Sum_{k>0} (-x)^prime(k)). - Vladeta Jovovic, Mar 29 2003
Extensions
More terms from Vladeta Jovovic, Mar 29 2003
Entry revised by N. J. A. Sloane, Dec 04 2006
Comments