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%I A264045 #8 Dec 16 2015 14:38:02
%S A264045 69,77,106,161,178,221,254,309,314,329,341,386,398,417,422,473,554,
%T A264045 662,674,689,758,794,934,974,998,1094,1121,1149,1169,1214,1294,1502,
%U A264045 1517,1522,1541,1569,1673
%N A264045 Numbers n such that n and n+5 are consecutive semiprimes.
%C A264045 Note that a(1)=69=A131109(k=5).
%H A264045 Charles R Greathouse IV, <a href="/A264045/b264045.txt">Table of n, a(n) for n = 1..10000</a>
%F A264045 a(n) >> n log n. - _Charles R Greathouse IV_, Nov 02 2015
%e A264045 a(1)=69=A001358(24) and a(1)+k=74=A001358(25).
%t A264045 Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,2000}],6,1], _?(#=={1,0,0,0,0,1}&)]] (* _Harvey P. Dale_, Dec 16 2015 *)
%o A264045 (PARI) is(n)=if(n%4==1, isprime((n+5)/2) && bigomega(n)==2, n%4==2 && isprime(n/2) && bigomega(n+5)==2) && bigomega(n+1)!=2 && bigomega(n+2)!=2 && bigomega(n+3)!=2 && bigomega(n+4)!=2 \\ _Charles R Greathouse IV_, Nov 02 2015
%Y A264045 Cf. A001358, A065516, A123375, A131109, A136196, A264043, A264044.
%K A264045 nonn
%O A264045 1,1
%A A264045 _Zak Seidov_, Nov 02 2015

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