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A361611 Lexicographically least increasing sequence of semiprimes a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also semiprimes.

%I A361611 #12 Apr 04 2023 19:48:32
%S A361611 4,10,25,94,115,206,221,298,391,478,511,526,551,586,655,694,703,758,
%T A361611 779,934,949,974,989,993,1126,1159,1418,1513,1522,1555,1594,1603,1658,
%U A361611 1679,1718,1769,2018,2051,2066,2105,2174,2195,2234,2319,2462,2501,2578,2587,2846,2867,2906,2931,2986,3007
%N A361611 Lexicographically least increasing sequence of semiprimes a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also semiprimes.
%H A361611 Robert Israel, <a href="/A361611/b361611.txt">Table of n, a(n) for n = 1..10000</a>
%e A361611 a(3) = 25 because with a(2) = 10, 25, 25 - 10 = 15 and 25 + 10 = 35 are all semiprimes, and none of the semiprimes between 10 and 25 work.
%p A361611 R:= 4: count:= 0: x:= 4:
%p A361611 for i from 5 while count < 100 do
%p A361611   if andmap(t -> numtheory:-bigomega(t)=2, [i,i+x,i-x]) then
%p A361611     R:= R,i; x:= i; count:= count+1
%p A361611   fi
%p A361611 od:
%p A361611 R;
%t A361611 s = {m=4};Do[p = m + 4; While[{2, 2, 2} != PrimeOmega[{p, m + p, p -
%t A361611 m}], p++]; AppendTo[s, m = p], {100}]; s
%Y A361611 Cf. A001358.
%K A361611 nonn
%O A361611 1,1
%A A361611 _Zak Seidov_ and _Robert Israel_, Mar 17 2023