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a(1) = 4; a(n) = smallest composite number greater than the sum of all previous terms.
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%I #8 Sep 14 2024 18:34:29

%S 4,6,12,24,48,95,190,380,760,1520,3040,6080,12160,24320,48640,97280,

%T 194560,389120,778240,1556480,3112960,6225920,12451840,24903680,

%U 49807360,99614720,199229440,398458880,796917760,1593835520,3187671040

%N a(1) = 4; a(n) = smallest composite number greater than the sum of all previous terms.

%C a(n) = 95*2^(n-6) for n > 5.

%H Harvey P. Dale, <a href="/A070232/b070232.txt">Table of n, a(n) for n = 1..1000</a>

%t a = {4}; Do[b = 1 + Plus @@ a; While[ PrimeQ[b], b++ ]; a = Append[a, b], {n, 2, 30}]; a

%t nxt[{t_,a_}]:=Module[{k=t+1},While[!CompositeQ[k],k++];{t+k,k}]; NestList[nxt,{4,4},30][[;;,2]] (* _Harvey P. Dale_, Sep 14 2024 *)

%Y Cf. A070218.

%K nonn

%O 1,1

%A _Amarnath Murthy_, May 05 2002

%E Edited by _Robert G. Wilson v_, May 06 2002