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%I #14 Nov 26 2015 18:06:07
%S 6,4,26,9,10,65,33,57,21,22,377,111,39,123,87,91,95,49,206,339,121,62,
%T 393,69,141,145,74,1141,362,93,94,95,291,505,209,106,215,219,111,339,
%U 115,1205,253,917,685,566,289,146,295,299,303,933,159,321,489,835,341
%N Semiprimes from partition of sequence of positive integers.
%C Partition the sequence of positive integers into groups of numbers that sum up to semiprimes: {1, 2, 3}, {4}, {5..8}, {9}, {10}, {11..15}, {16, 17}, {18..20}, {21}, {22}, {23..35}, {36..38}, {39}, {40..42}, {43, 44}, etc. Corresponding semiprimes are: 6, 4, 26, 9, 10, 65, 33, 57, 21, 22, 377, 111, 39, 123, 87, etc.
%C Is the sequence finite? See comment in A109411.
%H Zak Seidov, <a href="/A133837/b133837.txt">Table of n, a(n) for n = 1..10000</a>
%t s=Range[300];c=0;Label[1];i=1;p=s[[1]];While[i<Length[s]&&Plus@@Last/@FactorInteger[p]=/=2,i++;p=Plus@@Take[s,i]];(*Print[{i,p}] ;*)c++;a[c]=p;s=Drop[s,i];If[Length[s]>1,Goto[1]];Table[a[j],{j,c}]
%Y Cf. A109411.
%K nonn
%O 1,1
%A _Zak Seidov_, Sep 26 2007
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