A002123 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)

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

Offset

1,3

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 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).

Links

T. D. Noe, 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.

Index entries for sequences related to Goldbach conjecture

Prog

(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)
-- Reinhard Zumkeller, Mar 21 2014

Crossrefs

Cf. A065091, A061397.

Sequence in context: A326990 A037284 A225058 * A276408 A225744 A275393

Adjacent sequences: A002120 A002121 A002122 * A002124 A002125 A002126

Keyword

sign

Author

N. J. A. Sloane

Extensions

Extended with signs by T. D. Noe, Dec 05 2006

Status

approved