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A273879
Numbers k such that k and k+1 have 6 distinct prime factors.
5
11243154, 13516580, 16473170, 16701684, 17348330, 19286805, 20333495, 21271964, 21849905, 22054515, 22527141, 22754589, 22875489, 24031370, 25348070, 25774329, 28098245, 28618394, 28625960, 30259229, 31846269, 32642805
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
{k: k in A074969 and k+1 in A074969.} - R. J. Mathar, Jul 19 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
Numbers k such that k and k+1 have j distinct prime factors: A006549 (j=1, apart from the first term), A074851 (j=2), A140077 (j=3), A140078 (j=4), A140079 (j=5).
Sequence in context: A219749 A219750 A201253 * A321506 A253960 A253967
KEYWORD
nonn
AUTHOR
STATUS
approved