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A065305 Triangular array giving means of two odd primes: T(n,k) = (n-th prime + k-th prime)/2, n >= k >= 2.

%I A065305 #14 Oct 07 2015 04:53:10
%S A065305 3,4,5,5,6,7,7,8,9,11,8,9,10,12,13,10,11,12,14,15,17,11,12,13,15,16,
%T A065305 18,19,13,14,15,17,18,20,21,23,16,17,18,20,21,23,24,26,29,17,18,19,21,
%U A065305 22,24,25,27,30,31,20,21,22,24,25,27,28,30,33,34,37,22,23,24,26,27,29,30
%N A065305 Triangular array giving means of two odd primes: T(n,k) = (n-th prime + k-th prime)/2, n >= k >= 2.
%H A065305 Reinhard Zumkeller, <a href="/A065305/b065305.txt">First 125 rows of triangle, flattened</a>
%H A065305 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A065305 3; 4,5; 5,6,7; 7,8,9,11; ...
%p A065305 seq(seq((ithprime(i)+ithprime(j))/2,j=2..i),i=2..20)
%o A065305 (Haskell)
%o A065305 import Data.List (inits)
%o A065305 a065305 n k = a065305_tabl !! (n-2) !! (k - 1)
%o A065305 a065305_row n = a065305_tabl !! (n-2)
%o A065305 a065305_tabl = zipWith (map . (flip div 2 .) . (+))
%o A065305                        a065091_list $ tail $ inits a065091_list
%o A065305 -- _Reinhard Zumkeller_, Aug 02 2015, Jan 30 2012
%Y A065305 Cf. A065306.
%Y A065305 a(n, k) = A065342(n, k)/2 [but note different offsets]
%Y A065305 Cf. A098090 (left edge), A065091 (right edge), A000040.
%K A065305 easy,nonn,tabl
%O A065305 2,1
%A A065305 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001