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A363786 a(0) = 2. For n >= 1, a(n) is the least prime p such that a(n-1) + p has n prime factors counted with multiplicity.

%I A363786 #8 Jun 22 2023 06:03:59
%S A363786 2,3,3,5,11,37,59,229,347,421,3163,4517,1627,26021,14939,34213,64091,
%T A363786 378277,14939,3392933,146011,6931877,8796763,37340581,25573979,
%U A363786 238667173,113654363,1018807717,491141723,4743349669,8544205403,10246276517,491141723
%N A363786 a(0) = 2. For n >= 1, a(n) is the least prime p such that a(n-1) + p has n prime factors counted with multiplicity.
%F A363786 A001222(a(n-1) + a(n)) = n.
%e A363786 a(5) = 37 because a(4) + 37 = 48 = 2^4*3 has 5 prime factors counted with multiplicity.
%p A363786 R:= 2: t:= 2:
%p A363786 for n from 1 to 30 do
%p A363786   p:= 1:
%p A363786   do p:= nextprime(p)
%p A363786   until numtheory:-bigomega(t+p) = n;
%p A363786   R:= R,p;
%p A363786   t:= p;
%p A363786 od:
%p A363786 R;
%t A363786 s={2};Do[p=2;While[PrimeOmega[s[[-1]]+p]!=
%t A363786 k,p=NextPrime[p]];Print[p];AppendTo[s,p],{k,1,50}];
%Y A363786 Cf. A001222, A357713.
%K A363786 nonn
%O A363786 0,1
%A A363786 _Zak Seidov_ and _Robert Israel_, Jun 21 2023