login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113000 Numbers n such that n, n+1, n+2 and n+3 are 1,2,3,4-almost primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A065213 A100363 A142500 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

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