OFFSET

1,1

COMMENTS

"5-almost primes" that keep that property when incremented by 2. This sequence is to 5 as 4 is to A180150, as 3 is to A180117, as A092207 is to 2, and as A001359 is to 1. That is, this sequence is the 5th row of the infinite array A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity). The first row is the lesser of twin primes. The second row is the sequence such that m and m+2 are both semiprimes.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

EXAMPLE

a(1) = 270 because 270 = 2 * 3^3 * 5 is divisible by exactly 5 primes (counted with multiplicity), and so is 270+2 = 272 = 2^4 * 17.

MATHEMATICA

f[n_] := Plus @@ (Last@# & /@ FactorInteger@n); fQ[n_] := f[n] == 5 == f[n + 2]; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Aug 15 2010 *)

PROG

(PARI) for(x=2, 10^4, if(bigomega(x)==5&&bigomega(x+2)==5, print1(x", "))) \\ Zak Seidov, Aug 12 2010

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 12 2010

EXTENSIONS

Corrected and extended by Zak Seidov and R. J. Mathar, Aug 12 2010

STATUS

approved