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 A002120 a(1) = 0, a(2) = -2; for n > 2, a(n) + a(n-2) - a(n-3) - a(n-5) - ... - a(n-p) = (-1)^(n+1)*n if n is prime, otherwise = 0, where p = largest prime < n. (Formerly M0414 N0158) 5
 0, -2, 3, 2, 0, 1, 7, 2, -6, 8, 22, -7, 0, 33, 3, -14, 51, 46, -19, 12, 94, 42, -23, 113, 150, -54, 48, 345, 116, -109, 403, 498, -140, 219, 1057, 326, -259, 1271, 1641, -308, 656, 3396, 1161, -790, 4269, 5357, -987, 2257, 10934, 3958, -1986, 13678, 17278, -2492, 7447, 35569, 13778, -5860, 44368, 56403, -6405 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A289813 A050075 A247490 * A021435 A334358 A226556 Adjacent sequences:  A002117 A002118 A002119 * A002121 A002122 A002123 KEYWORD sign AUTHOR EXTENSIONS More terms from Vladeta Jovovic, May 08 2003 Edited by N. J. A. Sloane, Dec 03 2006 STATUS approved

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Last modified April 18 02:38 EDT 2021. Contains 343072 sequences. (Running on oeis4.)