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A207005
Numbers k such that omega(k) = omega(k - omega(k)) where omega(k) is the number of distinct primes dividing k.
2
1, 3, 4, 5, 8, 9, 12, 14, 17, 20, 22, 24, 26, 28, 32, 35, 36, 38, 40, 46, 48, 50, 52, 54, 56, 57, 58, 65, 74, 76, 77, 82, 87, 88, 93, 94, 95, 96, 98, 100, 105, 106, 108, 117, 118, 119, 124, 128, 135, 136, 143, 144, 145, 146, 147, 148, 155, 160, 161, 162, 164
OFFSET
1,2
COMMENTS
omega is the function in A001221. If there are infinitely many primes p such that p and 2p-1 are primes (see A005382), then this sequence is infinite. Proof: the numbers of the form 4p are in a subsequence if p and 2p-1 are both prime, because from the property that omega(4p) = 2 and omega(p(2p-1)) = 2, if n = 4p then omega(n-omega(n)) = omega(4p - 2) = omega(2(2p-1)) = 2 = omega(n).
LINKS
EXAMPLE
12 is in the sequence because omega(12) = 2, omega(12 - 2) = omega(10) = 2.
MATHEMATICA
Select[Range[10^4], PrimeNu[#]==PrimeNu[#-PrimeNu[#]]&]
CROSSREFS
Sequence in context: A178837 A217288 A212011 * A316976 A256173 A050070
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 14 2012
STATUS
approved