A371622 Primes p such that p - 2 and p + 2 have the same number of prime factors, counted with multiplicity.

5, 23, 37, 53, 67, 89, 113, 131, 157, 173, 211, 251, 277, 293, 307, 337, 379, 409, 449, 487, 491, 499, 503, 607, 631, 683, 701, 719, 751, 769, 787, 919, 929, 941, 953, 991, 1009, 1039, 1117, 1129, 1181, 1193, 1201, 1237, 1259, 1381, 1399, 1439, 1459, 1471, 1493, 1499, 1511, 1549, 1567, 1597, 1613

Offset: 1

Author

Zak Seidov and Robert Israel, Apr 01 2024

Keywords

• nonn

Comments

Primes p such that A001222(p - 2) = A001222(p + 2).

Examples

			a(2) = 23 is a term because 23 is prime and 23 - 2 = 21 = 3 * 7 and 23 + 2 = 25 = 5^2 are both products of 2 primes, counted with multiplicity.
		

Links

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

Crossrefs

Cf. A001222, A115103. Contains A063643, A063645 and A371651. Contained in A371656.

Programs

Maple

filter:= p -> isprime(p) and numtheory:-bigomega(p-2) = numtheory:-bigomega(p+2):
select(filter, [seq(i,i=3..10000,2)]);

Mathematica

s = {}; p = 3; Do[While[PrimeOmega[p - 2] != PrimeOmega[p + 2], p =
NextPrime[p]]; Print[p]; AppendTo[s, p]; p = NextPrime[p], {100}]; s