A065342 - OEIS

%I #22 Sep 10 2021 06:08:00

%S 4,5,6,7,8,10,9,10,12,14,13,14,16,18,22,15,16,18,20,24,26,19,20,22,24,

%T 28,30,34,21,22,24,26,30,32,36,38,25,26,28,30,34,36,40,42,46,31,32,34,

%U 36,40,42,46,48,52,58,33,34,36,38,42,44,48,50,54,60,62,39,40,42,44,48

%N Triangle of sum of two primes: prime(n)+prime(k) with n >= k >= 1.

%H Reinhard Zumkeller, <a href="/A065342/b065342.txt">First 125 rows of triangle, flattened</a>

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

%F T(n, k) = 2*A065305(n, k) [but note different offset].

%e Sequence starts 2+2; 3+2, 3+3; 5+2, 5+3, 5+5; etc. i.e. 4; 5,6; 7,8,10; ...

%e Triangle begins:

%e    4;

%e    5,  6;

%e    7,  8, 10;

%e    9, 10, 12, 14;

%e   13, 14, 16, 18, 22;

%e   ...

%o (Haskell)

%o import Data.List (inits)

%o a065342 n k = a065342_tabl !! (n-1) !! (k-1)

%o a065342_row n = a065342_tabl !! (n-1)

%o a065342_tabl = zipWith (map . (+)) a000040_list $ tail $ inits a000040_list

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

%o (PARI) row(n) = vector(n, k, prime(n)+prime(k)); \\ _Michel Marcus_, Sep 10 2021

%Y Cf. A052147 (left edge), A100484 (right edge), A000040.

%Y Cf. A087112.

%Y Cf. A065305.

%K nonn,tabl

%O 1,1

%A _Henry Bottomley_, Oct 30 2001