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%I #10 Feb 20 2023 07:50:56
%S 3,33,42,196,918,6640,24750,246078,781248,6565374,25227774,165009150,
%T 673932798,5268548608,25737162750,179511912448,818179991550,
%U 4228689854464,26455088693248,104384041582590,820632501420030
%N n-th natural number m such that m and m+2 are both divisible by exactly n primes (counted with multiplicity).
%C Main diagonal A[n,n] of A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity).
%C This is the main diagonal of the array mentioned in A180117, A180150, and A180151.
%C Row 1 = A001359 = the lesser of twin primes.
%C Row 2 = A092207 = Numbers n such that n and n+2 are semiprimes.
%C Row 3 = A180117 = m and m+2 are both divisible by exactly 3 primes (counted with multiplicity).
%C Row 4 = A180150 = m and m+2 are both divisible by exactly 4 primes (counted with multiplicity).
%C Row 5 = A180151 = m and m+2 are both divisible by exactly 5 primes (counted with multiplicity).
%e a(1) = 3 because 3 is the first natural number m such that m and m+2 are both divisible by exactly 1 prime (i.e., the first of the lesser of twin primes).
%e a(2) = 33 because that is the 2nd natural number m such that m and m+2 are both divisible by exactly 2 primes (i.e. 33 = 3 * 11 is semiprime and when 2 is added becomes 35 = 5 * 7 which is also semiprimes) the 1st such being 4.
%Y Cf. A001359, A092207, A180117, A180150, A180151.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 19 2010
%E Corrected and extended by _Jack Brennen_, _D. S. McNeil_ and _Ray Chandler_, Aug 19 2010
%E a(16)-a(21) from _Donovan Johnson_, Aug 27 2010
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