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A215217 Smaller member of a pair of sphenic twins, consecutive integers, each the product of three distinct primes.

%I A215217 #30 Jun 11 2019 00:25:45
%S A215217 230,285,429,434,609,645,741,805,902,969,986,1001,1022,1065,1085,1105,
%T A215217 1130,1221,1245,1265,1309,1310,1334,1406,1434,1442,1462,1490,1505,
%U A215217 1533,1581,1598,1605,1614,1634,1729,1742,1833,1885,1886,1946,2013,2014,2054,2085
%N A215217 Smaller member of a pair of sphenic twins, consecutive integers, each the product of three distinct primes.
%C A215217 455 is not a term of the sequence, since 455 = 5*7*13 is sphenic, i.e., the number of distinct prime factors is 3, though 456 = 2^3*3*19 has 3 distinct prime factors but is not sphenic, because the number of prime factors with repetition is 5 > 3.
%H A215217 Vincenzo Librandi, <a href="/A215217/b215217.txt">Table of n, a(n) for n = 1..1000</a>
%p A215217 Sphenics:= select(t -> (map(s->s[2],ifactors(t)[2])=[1,1,1]), {$1..10000}):
%p A215217 Sphenics intersect map(`-`,Sphenics,1); # _Robert Israel_, Aug 13 2014
%t A215217 Select[Range[2500], (PrimeNu[#] == PrimeOmega[#] == PrimeNu[#+1] == PrimeOmega[#+1] == 3)&] (* _Jean-François Alcover_, Apr 11 2014 *)
%t A215217 SequencePosition[Table[If[PrimeNu[n]==PrimeOmega[n]==3,1,0],{n,2500}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 02 2017 *)
%o A215217 (Haskell)
%o A215217 twinLow [] = []
%o A215217 twinLow [_] = []
%o A215217 twinLow (n : (m : ns))
%o A215217     | m == n + 1 = n : twinLow (m : ns)
%o A215217     | otherwise = twinLow (m : ns)
%o A215217 a215217 n = (twinLow a007304_list) !! (n - 1)
%o A215217 -- _Peter Dolland_, May 31 2019
%o A215217 (PARI) is_a033992(n) = omega(n)==3 && bigomega(n)==3
%o A215217 is(n) = is_a033992(n) && is_a033992(n+1) \\ _Felix Fröhlich_, Jun 10 2019
%Y A215217 Cf. A007304, A066509, A140077.
%K A215217 nonn
%O A215217 1,1
%A A215217 _Martin Renner_, Aug 06 2012