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%I #13 Feb 01 2017 01:35:32
%S 61,73,193,277,397,421,613,661,757,1093,1237,1453,1657,2137,2341,2593,
%T 2797,2917,3217,4177,4621,5233,6121,6133,6217,7057,7537,8101,8317,
%U 8353,8521,8677,8893,9013,9277,9721,9817,10357,10957,11161,11677,11701,12301
%N Numbers n such that n, n+1 and n+2 are 1,2,3-almost primes.
%C It's easy to see that all terms = 1 modulo 12. Primes p are {1,5,7,11} mod 12. Then p+1 = {2,6,8,12} mod 12 and only 2 mod 12 may give semiprime. Cf. A186696 for values of (a(n)-1)/12 = 5,6,16,23,33,35, etc.
%H Zak Seidov, <a href="/A112998/b112998.txt">Table of n, a(n) for n = 1..1000</a>
%e 61 is prime, 62=2*31 is semiprime, 63=3*3*7 is 3-almost prime.
%t Do[p=Prime[n];If[Total[FactorInteger[p+1]][[2]]==2&&Total[FactorInteger[p+2]][[2]]==3, Print[p]], {n, 1, 1000}];
%o (PARI) list(lim)=my(v=List(),L=(lim+2)\3,t); forprime(p=3,L\3, forprime(q=3,min(L\p,p), t=3*p*q-2; if(t%12==1 && isprime(t) && isprime((t+1)/2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 03 2006
%E Extended and edited by _Charles R Greathouse IV_, Apr 20 2010
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