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