OFFSET
1,1
COMMENTS
Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite (Theorem 2).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yildirim, Small gaps between almost primes, the parity problem and some conjectures of Erdős on consecutive integers, arXiv:0803.2636 [math.NT], 2008.
D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yildirim, Small gaps between almost primes, the parity problem and some conjectures of Erdős on consecutive integers, International Mathematics Research Notices 7 (2011), pp. 1439-1450.
FORMULA
a(1) = A138206(2). - R. J. Mathar, Jul 15 2023
EXAMPLE
13516580 = 2^2 * 5 * 7 * 11 * 67 * 131 and 13516581 = 3 * 13 * 17 * 19 * 29 * 37 so 13516580 is in this sequence.
MATHEMATICA
SequencePosition[PrimeNu[Range[3265*10^4]], {6, 6}][[All, 1]] (* Harvey P. Dale, Nov 20 2021 *)
PROG
(PARI) is(n)=omega(n)==6 && omega(n+1)==6
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Jun 02 2016
STATUS
approved