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A368648 Lexicographically earliest increasing sequence of semiprimes such that a(n) + a(n+1) is a semiprime, with a(0) = 4.

%I A368648 #7 Jan 12 2024 22:46:46
%S A368648 4,6,9,25,26,39,46,49,57,58,65,69,74,85,93,94,111,115,122,143,146,155,
%T A368648 159,187,194,201,202,205,206,209,213,214,237,265,278,287,299,323,326,
%U A368648 329,358,365,381,382,403,415,427,451,454,469,482,497,501,502,505,537,542,559,562,573,581,586,591,611
%N A368648 Lexicographically earliest increasing sequence of semiprimes such that a(n) + a(n+1) is a semiprime, with a(0) = 4.
%C A368648 The only case where two successive terms are even is 4, 6 at the start, since if 2*p and 2*q are semiprimes where p and q are odd primes, 2*p + 2*q is divisible by 4.
%H A368648 Robert Israel, <a href="/A368648/b368648.txt">Table of n, a(n) for n = 0..10000</a>
%e A368648 a(2) = 6 because 6 = 2 * 3 and 4 + 6 = 10 = 2 * 5 are semiprimes.
%e A368648 a(3) = 9 because 9 = 3 * 3 and 6 + 9 = 15 = 3 * 5 are semiprimes.
%e A368648 a(4) = 25 because 25 = 5 * 5 and 9 + 25 = 34 = 2 * 17 are semiprimes.
%p A368648 R:= 4: x:= 4: count:= 1:
%p A368648 for y from 5 do
%p A368648     if numtheory:-bigomega(y) = 2 and numtheory:-bigomega(x+y) = 2 then
%p A368648       R:= R,y; x:= y; count:= count+1;
%p A368648       if count = 100 then break fi
%p A368648     fi
%p A368648 od:
%p A368648 R;
%Y A368648 Cf. A001358, A361611.
%K A368648 nonn
%O A368648 0,1
%A A368648 _Zak Seidov_ and _Robert Israel_, Jan 02 2024