A002123 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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