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%I #18 Feb 27 2024 09:43:30
%S 134,597,614,898,982,998,1649,2045,2078,2126,2386,2705,2855,2935,3394,
%T 3418,3899,5533,5686,5959,6982,7721,8567,8986,9182,9722,9998,10342,
%U 10587,10862,10942,11015,11363,11602,11667,11962,13238,13606,14054,14138,14506,14614,15658,15802,15898,16138,16382
%N Semiprimes that are the sum of two successive semiprimes and also the sum of three successive semiprimes.
%H Robert Israel, <a href="/A370162/b370162.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 614 is a term because 614 = 2 * 307 is a semiprime, A001358(98) = 305 = 5 * 61 and A001358(99) = 309 = 3 * 103 are two successive semiprimes whose sum is 614, and A001358(65) = 203 = 7 * 29, A001358(66) = 205 = 5 * 41 and A001358(67) = 206 = 2 * 103 are three successive semiprimes whose sum is 614.
%p N:= 10^5: # for terms <= N
%p P:= select(isprime, [2,seq(i,i=3..N/2,2)]):
%p nP:= nops(P):
%p SP:= 0:
%p for i from 1 while P[i]^2 <= N do
%p m:= ListTools:-BinaryPlace(P, N/P[i]);
%p SP:= SP, op(P[i]*P[i..m]);
%p od:
%p SP:= sort([SP]):
%p SS:= ListTools:-PartialSums(SP):
%p SS2:= {seq(SS[i]-SS[i-2],i=3..nops(SS))}:
%p SS3:= {seq(SS[i]-SS[i-3],i=4..nops(SS))}:
%p A:=SS2 intersect SS3 intersect convert(SP,set):
%p sort(convert(A,list));
%Y Cf A001358, A118717. Intersection of A092192 and A131610.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Feb 26 2024
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