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.

2, 5, 13, 31, 61, 103, 157, 173, 181, 193, 211, 223, 239, 269, 313, 337, 353, 419, 487, 499, 577, 613, 631, 647, 677, 709, 727, 827, 857, 947, 1039, 1093, 1117, 1231, 1283, 1303, 1319, 1483, 1499, 1553, 1609, 1627, 1657, 1693, 1721, 1733, 1823, 1913, 1933, 1951, 2003, 2027, 2039, 2129, 2161, 2203

Offset: 1

Author

Zak Seidov and Robert Israel, Jun 07 2023

Keywords

• nonn

Examples

			a(2) = 5 because A001222(5-2) = A001222(5+2) = 1.
a(3) = 13 because A001222(13-5) = A001222(13+5) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A361611.

Programs

Maple

R:= 2: r:= 2:
for i from 1 to 100 do
    p:= nextprime(r);
    while numtheory:-bigomega(r+p) <> numtheory:-bigomega(p-r) do
      p:= nextprime(p)
    od;
    R:= R,p; r:= p;
od:
R;

Mathematica

s = {p = 2}; Do[q = NextPrime[p]; While[PrimeOmega[p + q]
!= PrimeOmega[q - p], q = NextPrime[q]]; AppendTo[s, p = q], {200}]; s

Formula

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