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

1,1

Comments

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).

Links

Table of n, a(n) for n=1..21.

Example

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.

Crossrefs

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

Sequence in context: A284064 A101968 A103862 * A084502 A248397 A069165

Adjacent sequences: A180242 A180243 A180244 * A180246 A180247 A180248

Keyword

nonn

Author

Jonathan Vos Post, Aug 19 2010

Extensions

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

Status

approved