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%I #11 Nov 20 2017 03:25:45
%S 58,91,123,142,161,205,278,473,566,614,706,718,802,838,851,889,1079,
%T 1211,1226,1238,1262,1286,1385,1415,1633,1714,1819,1891,1945,2005,
%U 2123,2147,2194,2217,2327,2374,2427,2563,2594,2653,2771,2815,2854,2947,2987,3118,3133,3151,3199,3214,3305,3379
%N Semiprimes that are the sum of six consecutive semiprimes.
%H Robert Israel, <a href="/A266451/b266451.txt">Table of n, a(n) for n = 1..10000</a>
%e 58 = A001358(21) = A001358(1) + ... + A001358(6) = 4+6+9+10+14+15,
%e 91 = A001358(31) = A001358(3) + ... + A001358(8) = 9+10+14+15+21+22.
%p N:= 10^4: # to get all terms where the 6 consecutive semiprimes <= N
%p P:= select(isprime, [2,seq(i,i=3..N/2,2)]): nP:= nops(P):
%p SP:= NULL:
%p for i from 1 to nP do
%p for j from 1 to nP while P[i]*P[j] <= N do od:
%p SP:= SP, op(map(`*`,P[i],P[1..j-1]));
%p od:
%p SP:= sort(convert({SP},list)): nSP:= nops(SP):
%p select(numtheory:-bigomega=2, [seq(convert(SP[i..i+5],`+`),i=1..nSP-5)]): # _Robert Israel_, Nov 19 2017
%t Select[(Total[#] & /@ Partition[Select[Range[4, 9999], 2 == PrimeOmega[#] &], 6, 1]), 2 == PrimeOmega[#] &]
%Y Cf. A001358, A092192, A131610, A158339, A254712.
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 29 2015
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