

A180117


Numbers n such that n and n+2 are both divisible by exactly 3 primes (counted with multiplicity).


4



18, 28, 42, 50, 66, 68, 76, 114, 170, 172, 186, 188, 236, 242, 244, 266, 273, 282, 284, 290, 316, 343, 354, 385, 402, 404, 410, 423, 426, 428, 434, 436, 475, 506, 596, 602, 603, 604, 637, 652, 663, 668, 722, 762, 775, 786, 788, 845, 890, 892, 906, 925, 962
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OFFSET

1,1


COMMENTS

"Triprimes" or "3almost primes" that keep that property when incremented by 2. Note that we don't care whether m+1 is also divisible by exactly 3 primes, as we first see with the triple (170, 171, 172). This sequence is to 3 as A092207 is to 2 and as A001359 is to 1. That is, this sequence is the 3rd row of the infinite array A[k,n] = nth natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity). The first row is the lesser of twin primes. The second row is the sequence such that m and m+2 are both semiprimes.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


FORMULA

{i such that i in A014612 and i+2 i in A014612}.


EXAMPLE

a(1) = 18 because 18 = 2*3*3 and 18+2 = 20 = 2*2*5 both have 3 prime divisors, counted with multiplicity.
a(2) = 28 because 28 = 2*2*7 and 28+2 = 30 = 2*3*5 both have 3 prime divisors, counted with multiplicity.


MATHEMATICA

#[[1, 1]]&/@(Select[Partition[Table[{n, PrimeOmega[n]}, {n, 1000}], 3, 1], #[[1, 2]]==#[[3, 2]]==3&]) (* Harvey P. Dale, Oct 20 2011 *)
SequencePosition[PrimeOmega[Range[1000]], {3, _, 3}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2017 *)


PROG

(PARI) is(n)=bigomega(n)==3 && bigomega(n+2)==3 \\ Charles R Greathouse IV, Jan 31 2017


CROSSREFS

Cf. A001359, A014612.
Sequence in context: A216259 A117101 A063840 * A167333 A259642 A045000
Adjacent sequences: A180114 A180115 A180116 * A180118 A180119 A180120


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Aug 10 2010


EXTENSIONS

More terms from R. J. Mathar, Aug 13 2010


STATUS

approved



