login
Triangular array giving means of two odd primes: T(n,k) = (n-th prime + k-th prime)/2, n >= k >= 2.
8

%I #14 Oct 07 2015 04:53:10

%S 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 18,19,13,14,15,17,18,20,21,23,16,17,18,20,21,23,24,26,29,17,18,19,21,

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

%H Reinhard Zumkeller, <a href="/A065305/b065305.txt">First 125 rows of triangle, flattened</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e 3; 4,5; 5,6,7; 7,8,9,11; ...

%p seq(seq((ithprime(i)+ithprime(j))/2,j=2..i),i=2..20)

%o (Haskell)

%o import Data.List (inits)

%o a065305 n k = a065305_tabl !! (n-2) !! (k - 1)

%o a065305_row n = a065305_tabl !! (n-2)

%o a065305_tabl = zipWith (map . (flip div 2 .) . (+))

%o a065091_list $ tail $ inits a065091_list

%o -- _Reinhard Zumkeller_, Aug 02 2015, Jan 30 2012

%Y Cf. A065306.

%Y a(n, k) = A065342(n, k)/2 [but note different offsets]

%Y Cf. A098090 (left edge), A065091 (right edge), A000040.

%K easy,nonn,tabl

%O 2,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001