A273879 Numbers k such that k and k+1 have 6 distinct prime factors.

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).

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