A370162 - OEIS

%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