This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002124 Number of compositions of n into a sum of odd primes. (Formerly M0154 N0062) 7
 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 4, 3, 7, 7, 8, 14, 15, 21, 28, 33, 47, 58, 76, 103, 125, 169, 220, 277, 373, 476, 616, 810, 1037, 1361, 1763, 2279, 2984, 3846, 5006, 6521, 8428, 10983, 14249, 18480, 24048, 31178, 40520, 52635, 68281, 88765, 115211, 149593, 194381, 252280, 327696, 425587, 552527, 717721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Arises in studying the Goldbach conjecture. The g.f. -(z-1)*(z+1)*(z**2+z+1)*(z**2-z+1)/(1-z**6-z**3-z**5-z**7+z**9) conjectured by Simon Plouffe in his 1992 dissertation is wrong. REFERENCES 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 N. J. A. Sloane, Table of n, a(n) for n = 0..1000 P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 300 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. 354-382] [The sequence i_n] Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. FORMULA a(0)=1, a(1)=a(2)=0; for n >= 3, a(n) = Sum_{ primes p with 3 <= p <= n} a(n-p). [MacMahon] G.f.: 1/( 1 - Sum_{k>=2}  x^A000040(k) ). [Joerg Arndt, Sep 30 2012] MAPLE A002124 := proc(n) coeff(series(1/(1-add(z^numtheory[ithprime](j), j=2..n)), z=0, n+1), z, n) end; M:=120; a:=array(0..M); a[0]:=1; a[1]:=0; a[2]:=0; for n from 3 to M do t1:=0; for k from 2 to n do p := ithprime(k); if p <= n then t1 := t1 + a[n-p]; fi; od: a[n]:=t1; od: [seq(a[n], n=0..M)]; # N. J. A. Sloane, after MacMahon, Dec 03 2006; used in A002125 MATHEMATICA a[0] = 1; a[1] = a[2] = 0; a[n_] := a[n] = (s = 0; p = 3; While[p <= n, s = s + a[n-p]; p = NextPrime[p]]; s); a /@ Range[0, 58] (* Jean-François Alcover, Jun 28 2011, after P. A. MacMahon *) PROG (Haskell) import Data.List (genericIndex) a002124 n = genericIndex a002124_list n a002124_list = 1 : f 1 [] a065091_list where    f x qs ps'@(p:ps)      | p <= x    = f x (p:qs) ps      | otherwise = sum (map (a002124 . (x -)) qs) : f (x + 1) qs ps' -- Reinhard Zumkeller, Mar 21 2014 CROSSREFS Cf. A002125, A023360, A024939, A077608. Cf. A065091. Sequence in context: A144254 A133310 A077608 * A097564 A128270 A151550 Adjacent sequences:  A002121 A002122 A002123 * A002125 A002126 A002127 KEYWORD nonn AUTHOR EXTENSIONS Better description and more terms from Philippe Flajolet, Nov 11 2002 Edited by N. J. A. Sloane, Dec 03 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 16:12 EDT 2019. Contains 328268 sequences. (Running on oeis4.)