

A180245


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


0



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

1,1


COMMENTS

Main diagonal A[n,n] of A[k,n] = nth 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 primes (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



