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A382933 Numbers k such that k, 2*m +- 3 and 3*m +- 2 are all semiprimes.

%I A382933 #13 Apr 17 2025 09:51:25
%S A382933 451,707,871,1313,1537,1819,1921,1969,2155,2195,2533,2599,2885,2993,
%T A382933 3265,3817,3883,3953,3997,4069,4105,4385,4555,4607,5599,5755,5771,
%U A382933 6155,6415,6773,7157,7453,7979,8185,8213,8251,8321,8333,8399,8531,9055,9077,9167,9335,9647,9953,9977,10121,10537
%N A382933 Numbers k such that k, 2*m +- 3 and 3*m +- 2 are all semiprimes.
%C A382933 All terms are odd.
%C A382933 The first term that is a square is a(241) = 49729 = 223^2.
%H A382933 Robert Israel, <a href="/A382933/b382933.txt">Table of n, a(n) for n = 1..10000</a>
%e A382933 a(3) = 871 because 871 = 13 * 67,
%e A382933 2 * 871 - 3 = 1739 = 37 * 47,
%e A382933 2 * 871 + 3 = 1745 = 5 * 349,
%e A382933 3 * 871 - 2 = 2611 = 7 * 373, and
%e A382933 3 * 871 + 2 = 2615 = 5 * 523 are all semiprimes.
%p A382933 filter:= m -> andmap(t -> numtheory:-bigomega(t)=2, [m,2*m-3,2*m+3,3*m-2,3*m+2]):
%p A382933 select(filter, [seq(i,i=1..20000,2)]);
%t A382933 s = {}; Do [ If [ {2, 2, 2, 2, 2} == PrimeOmega [{m, 2*m - 3, 2*m
%t A382933 + 3, 3*m - 2, 3*m + 2}], AppendTo [s, m]], {m, 5, 10^4, 2}]; s
%Y A382933 Cf. A001358.
%K A382933 nonn
%O A382933 1,1
%A A382933 _Zak Seidov_ and _Robert Israel_, Apr 15 2025