

A140077


Numbers n such that n and n+1 have 3 distinct prime factors.


16



230, 285, 429, 434, 455, 494, 560, 594, 609, 615, 644, 645, 650, 665, 740, 741, 759, 804, 805, 819, 825, 854, 860, 884, 902, 935, 945, 969, 986, 987, 1001, 1014, 1022, 1034, 1035, 1044, 1064, 1065, 1070, 1085, 1104, 1105, 1130, 1196, 1209, 1220, 1221
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OFFSET

1,1


COMMENTS

Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite.  Charles R Greathouse IV, Sep 14 2015
See A321503 for numbers n such that n & n+1 have at least 3 prime divisors, disjoint union of this and A321493, the terms of A321503 which are not in this sequence. A321493 has A140078 as a subsequence, which in turn is subsequence of A321504, and so on. Since n and n+1 can't share a prime factor, we have a(1) > sqrt(p(3+3)#) > A000196(A002110(3+3)). Note that A000196(A002110(3+4)) = A321493(1) exactly!  M. F. Hasler, Nov 13 2018


LINKS

Harvey P. Dale, 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 Erdos on consecutive integers, arXiv:0803.2636 [math.NT], 2008.


MATHEMATICA

a = {}; Do[If[Length[FactorInteger[n]] == 3 && Length[FactorInteger[n + 1]] == 3, AppendTo[a, n]], {n, 1, 100000}]; a (*Artur Jasinski*)
SequencePosition[PrimeNu[Range[1250]], {3, 3}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 27 2017 *)


PROG

(PARI) is(n)=omega(n)==3&&omega(n+1)==3 \\ Charles R Greathouse IV, Sep 14 2015


CROSSREFS

Cf. A074851, A140078, A140079.
Equals A321503 \ A321493.
Sequence in context: A122269 A171666 A321503 * A215217 A291617 A304389
Adjacent sequences: A140074 A140075 A140076 * A140078 A140079 A140080


KEYWORD

nonn


AUTHOR

Artur Jasinski, May 07 2008


STATUS

approved



