A124729 Numbers k such that k, k+1, k+2 and k+3 are products of 5 primes.

57967, 491875, 543303, 584647, 632148, 632149, 715374, 824523, 878875, 914823, 930123, 931623, 955448, 964143, 995874, 1021110, 1053351, 1070223, 1076535, 1099374, 1251963, 1289223, 1337355, 1380246, 1380247, 1436694, 1507623, 1517282, 1539873, 1669380, 1895222

Offset: 1

Author

Zak Seidov, Nov 05 2006

Keywords

• nonn

Comments

Subset of A045940 Numbers m such that factorizations of m through m+3 have same number of primes (including multiplicities).

There are no numbers k such that k, k+1, k+2 and k+3 are products of exactly 6 primes(?).

First counterexample: 8706123. - Charles R Greathouse IV, Jan 31 2017

Examples

			57967=7^3*13^2, 57968=2^4*3623, 57969=3^3*19*113, 57970=2*5*11*17*31 (all product of 5 primes, including multiplicities).
632148 is the first number such that n through n+4 are 5-almost primes.
		

Links

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

Crossrefs

Cf. A045940.

Cf. A124057, A124728 Numbers n such that n, n+1, n+2 and n+3 are products of exactly 3,4 primes.

Programs

Mathematica

SequencePosition[Table[If[PrimeOmega[n]==5,1,0],{n,19*10^5}],{1,1,1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 03 2019 *)

PARI

isok(n) = (bigomega(n) == 5) && (bigomega(n+1) == 5) && (bigomega(n+2) == 5) && (bigomega(n+3) == 5); \\ Michel Marcus, Oct 11 2013

Extensions

More terms from Michel Marcus, Oct 11 2013