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Search: id:A002121
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| A002121 |
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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).
(Formerly M0023 N0005)
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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Arises in studying the Goldbach conjecture.
The last negative term appears to be a(303). - T. D. Noe, Dec 05 2006
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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 g_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).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: 1/(1+Sum_{k>0} (-x)^prime(k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2003
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CROSSREFS
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Cf. A002100-A002125.
Sequence in context: A051734 A157898 A137430 this_sequence A118658 A165912 A071055
Adjacent sequences: A002118 A002119 A002120 this_sequence A002122 A002123 A002124
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2003
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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