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a(1) = 4; a(n) = smallest composite number different from the previous ones such that the sum of all the terms is a composite number.
1

%I #5 Mar 02 2024 15:49:24

%S 4,6,8,9,12,10,14,15,16,18,20,21,22,25,24,26,28,27,30,33,32,34,35,36,

%T 38,39,40,42,44,45,46,48,49,50,52,54,55,51,56,57,58,60,63,62,64,65,68,

%U 69,66,70,72,74,76,77,75,78,80,81,82,84,85,86,88,90,87,91,92,94,93,95

%N a(1) = 4; a(n) = smallest composite number different from the previous ones such that the sum of all the terms is a composite number.

%e 4+6+8+9 = 27. The next term is 12 instead of 10 as 27 +10 is a prime but 27 +12 = 39 is composite.

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Feb 26 2002

%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 21 2002

%E Offset corrected by _Sean A. Irvine_, Mar 02 2024