A113000 Numbers n such that n, n+1, n+2 and n+3 are 1,2,3,4-almost primes.

193, 421, 661, 1093, 1657, 2137, 2341, 2593, 6217, 7057, 8101, 9817, 12421, 12853, 15121, 16033, 16417, 17257, 17881, 19813, 20641, 21817, 25033, 25657, 27337, 28921, 30661, 31081, 31321, 31333, 32377, 35521, 36457, 38281, 40693, 45553

Offset

1,1

Comments

Subsequence of A112998: a(1) = 193 = A112998(3), a(2) = 421= A112998(6), a(3) = 661 = A112998(8). - Zak Seidov, Oct 14 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Example

193 is prime, 194=2*97 is semiprime, 195=3*5*13 is 3-almost prime, 196=2*2*7*7 is 4-almost prime.

Mathematica

Do[p=Prime[n]; If[Table[Total[FactorInteger[p+k]][[2]], {k, 3}]=={2, 3, 4}, Print[p]], {n, 1, 10000}]

Prog

(Magma)  [n: n in PrimesUpTo(5*10^4) | forall{k: k in [1..3] | &+[f[j, 2]: j in [1..#f]] eq k+1 where f is Factorization(n+k)}]; // Vincenzo Librandi, Sep 24 2012
(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) && bigomega(t+3)==4, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Crossrefs

Cf. A112998.

Sequence in context: A142500 A328137 A347636 * A105129 A140631 A142117

Adjacent sequences: A112997 A112998 A112999 * A113001 A113002 A113003

Keyword

nonn,easy

Author

Zak Seidov, Jan 03 2006

Extensions

Edited by Charles R Greathouse IV, Apr 20 2010

Status

approved