A268588 Numbers n such that n, n + 1, n + 2, n + 3 and n + 4 are products of exactly three primes.

602, 2522, 2523, 4202, 4921, 4922, 5034, 5282, 7730, 18241, 18242, 18571, 19129, 21931, 23161, 23305, 25203, 25553, 25554, 27290, 27291, 29233, 30354, 30793, 32035, 33843, 34561, 35714, 36001, 36835, 40313, 40314, 40394, 45265, 55361, 67609, 69667, 70202, 72721

Offset

1,1

Comments

Subsequence of A045941. - Zak Seidov, Jan 29 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..11023

Example

a(1) = 602: 602 = 2 * 7 * 43; 603 = 3 * 3 * 67; 604 = 2 * 2 * 151; 605 = 5 * 11 * 11; 606 = 2 * 3 * 101 are all products of three primes.
a(4) = 4202 : 4202 = 2 * 11 * 191; 4203 = 3 * 3 * 467; 4204 = 2 * 2 * 1051; 4205 = 5 * 29 * 29; 4206 = 2 * 3 * 701 are all products of three primes.

Maple

with(numtheory): A268588:= proc() if bigomega(n)=3 and bigomega(n+1)=3 and bigomega(n+2)=3 and bigomega(n+3)=3 and bigomega(n+4)=3 then RETURN (n); fi; end: seq(A268588(), n=1..100000);

Mathematica

Select[Range[100000], PrimeOmega[#] == 3 && PrimeOmega[# + 1] == 3 && PrimeOmega[# + 2] == 3 && PrimeOmega[# + 3] == 3 && PrimeOmega[# + 4] == 3 &]
SequencePosition[PrimeOmega[Range[73000]], {3, 3, 3, 3, 3}][[All, 1]] (* Harvey P. Dale, Sep 03 2021 *)

Prog

(PARI) for(n = 1, 50000, bigomega(n)==3 & bigomega(n+1)==3 & bigomega(n+2)==3 & bigomega(n+3)==3 & bigomega(n+4)==3 & print1(n, ", "))
(Magma) IsP3:=func< n | &+[k[2]: k in Factorization(n)] eq 3 >; [ n: n in [2..50000] | IsP3(n) and IsP3(n+1) and IsP3(n+2) and IsP3(n+3) and IsP3(n+4)];

Crossrefs

Cf. A056809, A113789, A124057, A045941.

Sequence in context: A252435 A363830 A045941 * A251462 A356893 A281561

Adjacent sequences: A268585 A268586 A268587 * A268589 A268590 A268591

Keyword

nonn

Author

K. D. Bajpai, Feb 07 2016

Extensions

Comment removed by Zak Seidov, Jan 29 2017

Status

approved