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A363513 a(1) = 2, then a(n) is the least prime p > a(n - 1) such that p + a(n-1) and p - a(n-1) have the same number of prime factors counted with multiplicity.

%I A363513 #26 Jun 11 2023 14:18:55
%S A363513 2,5,13,31,61,103,157,173,181,193,211,223,239,269,313,337,353,419,487,
%T A363513 499,577,613,631,647,677,709,727,827,857,947,1039,1093,1117,1231,1283,
%U A363513 1303,1319,1483,1499,1553,1609,1627,1657,1693,1721,1733,1823,1913,1933,1951,2003,2027,2039,2129,2161,2203
%N A363513 a(1) = 2, then a(n) is the least prime p > a(n - 1) such that p + a(n-1) and p - a(n-1) have the same number of prime factors counted with multiplicity.
%H A363513 Robert Israel, <a href="/A363513/b363513.txt">Table of n, a(n) for n = 1..10000</a>
%F A363513 A001222(a(n) - a(n-1)) = A001222(a(n) + a(n-1)).
%e A363513 a(2) = 5 because A001222(5-2) = A001222(5+2) = 1.
%e A363513 a(3) = 13 because A001222(13-5) = A001222(13+5) = 3.
%p A363513 R:= 2: r:= 2:
%p A363513 for i from 1 to 100 do
%p A363513     p:= nextprime(r);
%p A363513     while numtheory:-bigomega(r+p) <> numtheory:-bigomega(p-r) do
%p A363513       p:= nextprime(p)
%p A363513     od;
%p A363513     R:= R,p; r:= p;
%p A363513 od:
%p A363513 R;
%t A363513 s = {p = 2}; Do[q = NextPrime[p]; While[PrimeOmega[p + q]
%t A363513 != PrimeOmega[q - p], q = NextPrime[q]]; AppendTo[s, p = q], {200}]; s
%Y A363513 Cf. A001222, A361611.
%K A363513 nonn
%O A363513 1,1
%A A363513 _Zak Seidov_ and _Robert Israel_, Jun 07 2023