

A124729


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


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Subset of A045940 Numbers n such that factorizations of n through n+3 have same number of primes (including multiplicities).
There are no numbers n such that n, n+1, n+2 and n+3 are products of exactly 6 primes(?).
First counterexample: 8706123.  Charles R Greathouse IV, Jan 31 2017


LINKS

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


EXAMPLE

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 5almost primes.


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 *)


PROG

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


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.
Sequence in context: A031861 A119887 A188256 * A345565 A345820 A184372
Adjacent sequences: A124726 A124727 A124728 * A124730 A124731 A124732


KEYWORD

nonn


AUTHOR

Zak Seidov, Nov 05 2006


EXTENSIONS

More terms from Michel Marcus, Oct 11 2013


STATUS

approved



