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).
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).
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
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Aug 19 2010
EXTENSIONS
a(16)-a(21) from Donovan Johnson, Aug 27 2010
STATUS
approved