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A259756 Numbers n such that numbers n through n+6 are the product of exactly three (not necessarily distinct) primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)