1,1

n such that n, n+1, n+2 and n+3 are 3-almost primes. Subset of A113789 Numbers n such that n, n+1 and n+2 are products of exactly 3 primes. A067813 has some runs of up to 7 consecutive 3-almost primes (i.e. starting 211673). But there cannot be 8 consecutive 3-almost primes, as every run of 8 consecutive positive integers contains exactly one multiple of 8 = 2^3, and only 8 of all positive multiples of 8 is a 3-almost prime (i.e. all larger multiples have at least 4 prime factors, with multiplicity).

A subset of A045940. - Zak Seidov, Nov 05 2006 - Zak Seidov, Nov 05 2006

D. W. Wilson, Table of n, a(n) for n = 1..10000

n, n+1, n+2, and n+3 are all elements of A014612. n and n+1 are elements of A113789.

a(1) = 602 because 602 = 2 * 7 * 43 and 603 = 3^2 * 67 and 604 = 2^2 * 151 and 605 = 5 * 11^2 are all 3-almost primes.

a(2) = 603 because 603 = 3^2 * 67 and 604 = 2^2 * 151 and 605 = 5 * 11^2 and 606 = 2 * 3 * 101 are all 3-almost primes.

a(3) = 1083 because 1083 = 3 * 19^2 and 1084 = 2^2 * 271 and 1085 = 5 * 7 * 31 and 1086 = 2 * 3 * 181 are all 3-almost primes.

a(4) = 2012 because 2012 = 2^2 * 503, 2013 = 3 * 11 * 61, 2014 = 2 * 19 * 53, 2015 = 5 * 13 * 31.

a(5) = 2091 because 2091 = 3 * 17 * 41, 2092 = 2^2 * 523, 2093 = 7 * 13 * 23, 2094 = 2 * 3 * 349.

with(numtheory): a:=proc(n) if bigomega(n)=3 and bigomega(n+1)=3 and bigomega(n+2)=3 and bigomega(n+3)=3 then n else fi end: seq(a(n), n=1..15000); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 07 2006

Cf. A000040, A014612, A056809, A067813, A113789.

Cf. A045940.

Adjacent sequences: A124054 A124055 A124056 this_sequence A124058 A124059 A124060

Sequence in context: A094231 A107440 A045940 this_sequence A045941 A069473 A066785

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 03 2006

More terms from Zak Seidov, Nov 05 2006

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 07 2006