A363513 - OEIS

%I #26 Jun 11 2023 14:18:55

%S 2,5,13,31,61,103,157,173,181,193,211,223,239,269,313,337,353,419,487,

%T 499,577,613,631,647,677,709,727,827,857,947,1039,1093,1117,1231,1283,

%U 1303,1319,1483,1499,1553,1609,1627,1657,1693,1721,1733,1823,1913,1933,1951,2003,2027,2039,2129,2161,2203

%N 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 Robert Israel, <a href="/A363513/b363513.txt">Table of n, a(n) for n = 1..10000</a>

%F A001222(a(n) - a(n-1)) = A001222(a(n) + a(n-1)).

%e a(2) = 5 because A001222(5-2) = A001222(5+2) = 1.

%e a(3) = 13 because A001222(13-5) = A001222(13+5) = 3.

%p R:= 2: r:= 2:

%p for i from 1 to 100 do

%p     p:= nextprime(r);

%p     while numtheory:-bigomega(r+p) <> numtheory:-bigomega(p-r) do

%p       p:= nextprime(p)

%p     od;

%p     R:= R,p; r:= p;

%p od:

%p R;

%t s = {p = 2}; Do[q = NextPrime[p]; While[PrimeOmega[p + q]

%t != PrimeOmega[q - p], q = NextPrime[q]]; AppendTo[s, p = q], {200}]; s

%Y Cf. A001222, A361611.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Jun 07 2023