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Search: id:A002120
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| A002120 |
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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)
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Arises in studying the Goldbach conjecture.
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REFERENCES
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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]
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = (-1)^(n+1)*n*A010051(n)+Sum_{k=1..n-1} (-1)^(n-k+1)*A010051(n-k)*a(k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 08 2003
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MAPLE
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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)];
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CROSSREFS
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Adjacent sequences: A002117 A002118 A002119 this_sequence A002121 A002122 A002123
Sequence in context: A079757 A071493 A050075 this_sequence A021435 A007325 A056619
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KEYWORD
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sign
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), May 08 2003
Edited by njas, Dec 03 2006
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