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 A117929 Number of partitions of n into 2 distinct primes. 9
 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 2, 0, 3, 1, 2, 0, 2, 0, 3, 1, 2, 1, 3, 0, 4, 0, 1, 1, 3, 0, 4, 1, 3, 1, 3, 0, 5, 1, 4, 0, 3, 0, 5, 1, 3, 0, 3, 0, 6, 1, 2, 1, 5, 0, 6, 0, 2, 1, 5, 0, 6, 1, 4, 1, 5, 0, 7, 0, 4, 1, 4, 0, 8, 1, 4, 0, 4, 0, 9, 1, 4, 0, 4, 0, 7, 0, 3, 1, 6, 0, 8, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS Number of distinct rectangles with prime length and width such that L + W = n, W < L. For example, a(16) = 2; the two rectangles are 3 X 13 and 5 X 11. - Wesley Ivan Hurt, Oct 29 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA G.f.: Sum_{j>0} Sum_{i=1..j-1} x^(p(i)+p(j)), where p(k) is the k-th prime. G.f.: A(x)^2/2 - A(x^2)/2 where A(x) = Sum_{p in primes} x^p. - Geoffrey Critzer, Nov 21 2012 a(n) = [x^n*y^2] Product_{i>=1} (1+x^prime(i)*y). - Alois P. Heinz, Nov 22 2012 a(n) = Sum_{i=2..floor((n-1)/2)} A010051(i) * A010051(n-i). - Wesley Ivan Hurt, Oct 29 2017 EXAMPLE a(24) = 3 because we have [19,5], [17,7] and [13,11]. MAPLE g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j-1), j=1..35): gser:=series(g, x=0, 130): seq(coeff(gser, x, n), n=1..125); MATHEMATICA l = {}; For[n = 1, n <= 1000, n++, c = 0; For[k = 1, Prime[k] < n/2, k++, If[PrimeQ[n - Prime[k]], c = c + 1] ]; AppendTo[l, c] ] l (* Jake Foster, Oct 27 2008 *) Table[Count[IntegerPartitions[n, {2}], _?(AllTrue[#, PrimeQ]&&#[[1]]!= #[[2]] &)], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 26 2020 *) PROG (PARI) a(n)=my(s); forprime(p=2, (n-1)\2, s+=isprime(n-p)); s \\ Charles R Greathouse IV, Feb 26 2014 CROSSREFS Cf. A010051, A045917, A061358, A073610. Column k=2 of A219180. - Alois P. Heinz, Nov 13 2012 Sequence in context: A325538 A343422 A238417 * A306439 A107455 A039701 Adjacent sequences:  A117926 A117927 A117928 * A117930 A117931 A117932 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Apr 03 2006 STATUS approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)