OFFSET
1,2
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 e_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
N. J. A. Sloane, Table of n, a(n) for n = 1..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
a(n) = (-1)^(n+1)*n*A010051(n)+Sum_{k=1..n-1} (-1)^(n-k+1)*A010051(n-k)*a(k). - Vladeta Jovovic, May 08 2003
MAPLE
M:=90; e:=array(0..M); e[1]:=0; e[2]:=-2; for n from 3 to M do t1:=-e[n-2]; if isprime(n) then t1:=t1+(-1)^(n+1)*n; fi; for k from 2 to n do p := ithprime(k); if p < n then t1 := t1 + e[n-p]; fi; od: e[n]:=t1; od: [seq(e[n], n=1..M)];
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, May 08 2003
Edited by N. J. A. Sloane, Dec 03 2006
STATUS
approved