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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 A226556 A007325

Adjacent sequences:  A002117 A002118 A002119 * A002121 A002122 A002123

KEYWORD

sign

AUTHOR

N. J. A. Sloane.

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 October 16 23:45 EDT 2019. Contains 328103 sequences. (Running on oeis4.)