A259756 Numbers n such that numbers n through n+6 are the product of exactly three (not necessarily distinct) primes.
211673, 298433, 381353, 460801, 506521, 568729, 690593, 705953, 737633, 741305, 921529, 1056529, 1088521, 1105553, 1141985, 1362313, 2016721, 2270633, 2369809, 2535721, 2590985, 2688833, 2956681, 2983025, 3085201, 3112193, 3147553, 3269161
Offset: 1
Keywords
Examples
211673=7*11*2749, 211674=2*3*35279, 211675=5*5*8467, 211676=2*2*52919, 211677=3*37*1907, 211678=2*109*971, 211679=13*19*857.
Links
- Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 4000 from Seidov)
Programs
-
Maple
W:= numtheory:-bigomega: select(t -> isprime((t+3)/4) and W(t) = 3 and W(t+1) = 3 and W(t+2) = 3 and W(t+4) = 3 and W(t+5) = 3 and W(t+6) = 3, [seq(i, i=1..10^7, 8)]); # Robert Israel, Nov 24 2015
-
Mathematica
SequencePosition[PrimeOmega[Range[327*10^4]],{3,3,3,3,3,3,3}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 12 2019 *) -
PARI
forcomposite(n=1, 4*10^6, if(bigomega(n)==3 && bigomega(n+1)==3 && bigomega(n+2)==3 && bigomega(n+3)==3 && bigomega(n+4)==3 && bigomega(n+5)==3 && bigomega(n+6)==3, print1(n, ", "))) \\ Altug Alkan, Nov 08 2015
-
PARI
{(bo(n)=bigomega(n));n=211673-8;for(i=1,20000,n=n+8;while((a=bo(n))<>3||!isprime((n+3)/4),n=n+8);if(a==bo(n+1)&& a==bo(n+2)&&a==bo(n+4)&&a==bo(n+5)&&a==bo(n+6),print1(n",")))}\\ Zak Seidov, Jul 27 2016 -
PARI
list(lim)=my(v=List(), ct=6, is); forfactored(n=211679, lim\1+6, is=vecsum(n[2][, 2])==3; if(is, if(ct++==7, listput(v, n[1]-6)), ct=0)); Vec(v) \\ Charles R Greathouse IV, Jun 26 2019
Comments