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A368786 a(n) is the first prime p such that, if q are r are the next two primes, p + r, p + q, q + r and p + q + r all have n prime divisors, counted with multiplicity.

%I A368786 #11 Jan 12 2024 22:47:31
%S A368786 1559,4073,45863,1369133,82888913,754681217,118302786439
%N A368786 a(n) is the first prime p such that, if q are r are the next two primes, p + r, p + q, q + r and p + q + r all have n prime divisors, counted with multiplicity.
%C A368786 a(n) is the first term p of A368785 such that A001222(A013634(p)) = n.
%e A368786 a(5) = 45863 because 45863, 45869, 45887 are consecutive primes with
%e A368786 45863 + 45869 = 91732 = 2^2 * 17 * 19 * 71,
%e A368786 45863 + 45887 = 91750 = 2 * 5^3 * 367,
%e A368786 45869 + 45887 = 91756 = 2^2 * 7 * 29 * 113, and
%e A368786 45863 + 45869 + 45887 = 137619 = 3^4 * 1699
%e A368786 all have 5 prime divisors, counted with multiplicity, and 45763 is the least prime that works.
%p A368786 V:= Array(3..8): count:= 0:
%p A368786 p:= 2: q:= 3: r:= 5: v:= numtheory:-bigomega(q+r);
%p A368786 while count < 6 do
%p A368786   p:= q; q:= r; r:= nextprime(r);
%p A368786   w:= numtheory:-bigomega(q+r);
%p A368786   if (w > 7 or V[w] = 0) and w = v and numtheory:-bigomega(p+r) = v and numtheory:-bigomega(p+q+r) = v then
%p A368786     V[w]:= p; count:= count+1;
%p A368786     fi;
%p A368786   v:= w;
%p A368786 od:
%p A368786 convert(V,list);
%Y A368786 Cf. A001222, A013634, A368785.
%K A368786 nonn,more
%O A368786 3,1
%A A368786 _Zak Seidov_ and _Robert Israel_, Jan 05 2024
%E A368786 a(9) from _Daniel Suteu_, Jan 05 2024