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 A002125 a(n) = Sum_{k=0..n} f(k)*f(n-k) where f(k) = A002124(k). (Formerly M0024 N0006) 3
 1, 0, 0, 2, 0, 2, 3, 2, 6, 4, 9, 14, 11, 26, 29, 34, 62, 68, 99, 140, 169, 252, 322, 430, 607, 764, 1059, 1424, 1845, 2546, 3344, 4442, 6002, 7876, 10575, 14058, 18575, 24878, 32842, 43630, 58073, 76658, 101913, 134964, 178468, 236776, 312874, 414094, 547947, 723646 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Arises in studying the Goldbach conjecture. 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. 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. [The sequence I_n] FORMULA G.f.: 1/(1 - Sum_{k>=2} x^prime(k))^2. - Ilya Gutkovskiy, Apr 11 2017 MAPLE M:=120; f:=array(0..M); f[0]:=1; f[1]:=0; f[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 + f[n-p]; fi; od: f[n]:=t1; od: # f is A002124 A002125:=array(0..M); for n from 0 to M do A002125[n]:=add(f[t]*f[n-t], t=0..n); od: [seq(A002125[n], n=0..M)]; MATHEMATICA CoefficientList[Series[1/(1 - Sum[x^Prime[k], {k, 2, 50}])^2, {x, 0, 50}], x] (* Indranil Ghosh, Apr 12 2017 *) PROG (Haskell) a002125 n = a002125_list !! n a002125_list = uncurry conv \$ splitAt 1 a002124_list where    conv xs (z:zs) = sum (zipWith (*) xs \$ reverse xs) : conv (z:xs) zs -- Reinhard Zumkeller, Mar 21 2014 CROSSREFS Sequence in context: A212184 A033769 A074660 * A171731 A185815 A003987 Adjacent sequences:  A002122 A002123 A002124 * A002126 A002127 A002128 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Dec 03 2006 STATUS approved

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Last modified October 20 23:39 EDT 2018. Contains 316405 sequences. (Running on oeis4.)