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 A061358 Number of ways of writing n = p+q with p, q primes and p >= q. 52
 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 3, 0, 3, 1, 3, 0, 2, 0, 3, 1, 2, 1, 4, 0, 4, 0, 2, 1, 3, 0, 4, 1, 3, 1, 4, 0, 5, 1, 4, 0, 3, 0, 5, 1, 3, 0, 4, 0, 6, 1, 3, 1, 5, 0, 6, 0, 2, 1, 5, 0, 6, 1, 5, 1, 5, 0, 7, 0, 4, 1, 5, 0, 8, 1, 5, 0, 4, 0, 9, 1, 4, 0, 5, 0, 7, 0, 3, 1, 6, 0, 8, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS For an odd number n, a(n) = 0 if n-2 is not a prime else a(n) = 1. For n>1, a(2n) is at least 1, according to Goldbach's conjecture. a(A014092(n)) = 0; a(A014091(n)) > 0; a(A067187(n)) = 1. - Reinhard Zumkeller, Nov 22 2004 Number of partitions of n into two primes. Number of unordered ways of writing n as the sum of two primes. a(2*n) = A068307(2*n+2). [Reinhard Zumkeller, Aug 08 2009] 4*a(n) is the total number of divisors of all primes p and q such that n=p+q and p>=q. - Wesley Ivan Hurt, Mar 05 2016 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Sum_{j>0} Sum_{i=1..j} x^(p(i)+p(j)), where p(k) is the k-th prime. - Emeric Deutsch, Apr 03 2006 A065577(n) = a(10^n). From Wesley Ivan Hurt, Jan 04 2013: (Start) a(n) = Sum_{i=1..floor(n/2)} A010051(i) * A010051(n-i). a(n) = Sum_{i=1..floor(n/2)} floor((A010051(i) + A010051(n-i))/2). (End) EXAMPLE a(22) = 3 because 22 can be written as 3+19, 5+17 and 11+11. MAPLE g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j), j=1..30): gser:=series(g, x=0, 110): seq(coeff(gser, x, n), n=0..105); # Emeric Deutsch, Apr 03 2006 MATHEMATICA a[n_] := Length[Select[n - Prime[Range[PrimePi[n/2]]], PrimeQ]]; Table[a[n], {n, 0, 100}] (* Paul Abbott, Jan 11 2005 *) With[{nn=110}, CoefficientList[Series[Sum[x^(Prime[i]+Prime[j]), {j, nn}, {i, j}], {x, 0, nn}], x]] (* Harvey P. Dale, Aug 17 2017 *) PROG (PARI) a(n)=my(s); forprime(q=2, n\2, s+=isprime(n-q)); s \\ Charles R Greathouse IV, Mar 21 2013 (Python) from sympy import primerange, isprime, floor def a(n):     s=0     for q in primerange(2, n//2 + 1): s+=isprime(n - q)     return s print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 30 2017 (MAGMA) [#RestrictedPartitions(n, 2, {p:p in PrimesUpTo(1000)}):n in [0..100] ] // Marius A. Burtea, Jan 19 2019 CROSSREFS a(2n) is A045917. Cf. A067187, A067188, A067189, A067190, A067191, A063610, A073610, A107318. Column k=2 of A117278. Sequence in context: A156542 A307990 A066360 * A025866 A259920 A048881 Adjacent sequences:  A061355 A061356 A061357 * A061359 A061360 A061361 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Apr 28 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), May 15 2001 Comments edited by Zak Seidov, May 28 2014 STATUS approved

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Last modified August 15 10:43 EDT 2020. Contains 336492 sequences. (Running on oeis4.)