A180151 -id:A180151 - cp's OEIS frontend

A180245 n-th natural number m such that m and m+2 are both divisible by exactly n primes (counted with multiplicity).

3, 33, 42, 196, 918, 6640, 24750, 246078, 781248, 6565374, 25227774, 165009150, 673932798, 5268548608, 25737162750, 179511912448, 818179991550, 4228689854464, 26455088693248, 104384041582590, 820632501420030

Offset: 1

Jonathan Vos Post, Aug 19 2010

nonn

Main diagonal A[n,n] of A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity).
This is the main diagonal of the array mentioned in A180117, A180150, and A180151.
Row 1 = A001359 = the lesser of twin primes.
Row 2 = A092207 = Numbers n such that n and n+2 are semiprimes.
Row 3 = A180117 = m and m+2 are both divisible by exactly 3 primes (counted with multiplicity).
Row 4 = A180150 = m and m+2 are both divisible by exactly 4 primes (counted with multiplicity).
Row 5 = A180151 = m and m+2 are both divisible by exactly 5 primes (counted with multiplicity).

			a(1) = 3 because 3 is the first natural number m such that m and m+2 are both divisible by exactly 1 prime (i.e., the first of the lesser of twin primes).
a(2) = 33 because that is the 2nd natural number m such that m and m+2 are both divisible by exactly 2 primes (i.e. 33 = 3 * 11 is semiprime and when 2 is added becomes 35 = 5 * 7 which is also semiprimes) the 1st such being 4.

Cf. A001359, A092207, A180117, A180150, A180151.

Corrected and extended by Jack Brennen, D. S. McNeil and Ray Chandler, Aug 19 2010

a(16)-a(21) from Donovan Johnson, Aug 27 2010

cp's OEIS Frontend

A180245 n-th natural number m such that m and m+2 are both divisible by exactly n primes (counted with multiplicity).

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions