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A112998 Numbers n such that n, n+1 and n+2 are 1,2,3-almost primes. 9
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

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 * A118162 A217076 A281960

Adjacent sequences:  A112995 A112996 A112997 * A112999 A113000 A113001

KEYWORD

nonn

AUTHOR

Zak Seidov, Jan 03 2006

EXTENSIONS

Extended and edited by Charles R Greathouse IV, Apr 20 2010

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.