A207005 Numbers k such that omega(k) = omega(k - omega(k)) where omega(k) is the number of distinct primes dividing k.

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

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Cf. A001221, A005382.

Sequence in context: A178837 A217288 A212011 * A316976 A256173 A050070

Adjacent sequences: A207002 A207003 A207004 * A207006 A207007 A207008

Keyword

nonn

Author

Michel Lagneau, Feb 14 2012

Status

approved