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A112998
Numbers n such that n, n+1 and n+2 are 1,2,3-almost primes.
12
61, 73, 193, 277, 397, 421, 613, 661, 757, 1093, 1237, 1453, 1657, 2137, 2341, 2593, 2797, 2917, 3217, 4177, 4621, 5233, 6121, 6133, 6217, 7057, 7537, 8101, 8317, 8353, 8521, 8677, 8893, 9013, 9277, 9721, 9817, 10357, 10957, 11161, 11677, 11701, 12301
OFFSET
1,1
COMMENTS
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.
EXAMPLE
61 is prime, 62=2*31 is semiprime, 63=3*3*7 is 3-almost prime.
MATHEMATICA
Do[p=Prime[n]; If[Total[FactorInteger[p+1]][[2]]==2&&Total[FactorInteger[p+2]][[2]]==3, Print[p]], {n, 1, 1000}];
PROG
(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
CROSSREFS
Sequence in context: A033236 A260808 A141457 * A339778 A328160 A118162
KEYWORD
nonn
AUTHOR
Zak Seidov, Jan 03 2006
EXTENSIONS
Extended and edited by Charles R Greathouse IV, Apr 20 2010
STATUS
approved