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

1,1

Comments

All terms are == 1 (mod 8). There are no sets of 8 consecutive integers all 3-almost primes.

Note that a(1) = A067813(6). - Michel Marcus, Nov 24 2015

Links

Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 4000 from Seidov)

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A259504 and A014612. Cf. A067813.

Sequence in context: A097021 A236086 A123103 * A251511 A252880 A158993

Adjacent sequences: A259753 A259754 A259755 * A259757 A259758 A259759

Keyword

nonn

Author

Zak Seidov, Nov 08 2015

Status

approved