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A273879 Numbers k such that k and k+1 have 6 distinct prime factors. 3
11243154, 13516580, 16473170, 16701684, 17348330, 19286805, 20333495, 21271964, 21849905, 22054515, 22527141, 22754589, 22875489, 24031370, 25348070, 25774329, 28098245, 28618394, 28625960, 30259229, 31846269, 32642805 (list; graph; refs; listen; history; text; internal format)
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.

EXAMPLE

13516580 = 2^2 * 5 * 7 * 11 * 67 * 131 and 13516581 = 3 * 13 * 17 * 19 * 29 * 37 so 13516580 is in this sequence.

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).

Cf. A006049, A093548.

Sequence in context: A219749 A219750 A201253 * A321506 A253960 A253967

Adjacent sequences:  A273876 A273877 A273878 * A273880 A273881 A273882

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Jun 02 2016

STATUS

approved

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Last modified August 7 11:56 EDT 2020. Contains 336276 sequences. (Running on oeis4.)