login
A371622
Primes p such that p - 2 and p + 2 have the same number of prime factors, counted with multiplicity.
3
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
1,1
COMMENTS
Primes p such that A001222(p - 2) = A001222(p + 2).
LINKS
EXAMPLE
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.
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
CROSSREFS
Cf. A001222, A115103. Contains A063643, A063645 and A371651. Contained in A371656.
Sequence in context: A050906 A195974 A098421 * A044447 A242215 A061240
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Apr 01 2024
STATUS
approved