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

1,1

Comments

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

Links

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

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

Adjacent sequences: A371619 A371620 A371621 * A371623 A371624 A371635

Keyword

nonn

Author

Zak Seidov and Robert Israel, Apr 01 2024

Status

approved