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A002123
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a(1) = 0, a(2) = 0; for n > 2, a(n) - a(n-3) - a(n-5) - ... - a(n-p) = n if n is prime, otherwise = 0, where p = largest prime < n.
(Formerly M2198 N0876)
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1
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0, 0, 3, 0, 5, -3, 7, -8, 3, -15, 22, -15, 39, -35, 38, -72, 85, -111, 152, -175, 241, -308, 414, -551, 655, -897, 1164, -1463, 2001, -2538, 3286, -4296, 5503, -7259, 9357, -12147, 15910, -20406, 26640, -34703, 44854, -58481, 75809, -98340
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OFFSET
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1,3
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COMMENTS
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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 f_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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PROG
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(Haskell)
import Data.List (genericIndex)
a002123 n = genericIndex a002123_list (n - 1)
a002123_list = 0 : 0 : f 3 where
f x = y : f (x + 1) where
y = a061397 x -
sum (map (a002123 . (x -)) $ takeWhile (< x) a065091_list)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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Extended with signs by T. D. Noe, Dec 05 2006
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STATUS
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approved
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