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n-th row of the following triangle contains n even numbers such that every sum of n-1 of them + 1 is a prime. Sequence contains the triangle by rows.
2

%I #11 Apr 04 2015 21:50:42

%S 2,2,4,2,4,8,2,4,10,16,2,4,8,14,16,2,4,8,10,22,64,2,4,8,10,14,20,1822,

%T 2,4,8,10,14,20,38,5564,2,4,8,10,14,20,22,28,88712,2,4,8,10,14,20,22,

%U 28,58,855574,2,4,8,10,14,20,22,28,32,38,74266102,2,4,8,10,14,20,22,28,32

%N n-th row of the following triangle contains n even numbers such that every sum of n-1 of them + 1 is a prime. Sequence contains the triangle by rows.

%C For n =4, the third term is 10 and not 6 as then there is no number that qualifies for the fourth place. As for every k one of the numbers 2+k, 4+k or 6+k is divisible by 3.

%C We assume that for each row we want the lexicographically earliest possible set of even numbers. - _Joshua Zucker_, May 03 2006

%H T. Forbes, <a href="http://anthony.d.forbes.googlepages.com/adf.htm">Smallest prime k-tuplets</a> gives useful data for extending this sequence.

%e 2

%e 2 4

%e 2 4 8

%e 2 4 10 16

%e ...

%Y Cf. A083780, A083781.

%K nonn,tabl

%O 1,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 07 2003

%E More terms from _Joshua Zucker_, May 03 2006