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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
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
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 5-almost 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
KEYWORD
nonn
AUTHOR
Zak Seidov, Nov 05 2006
EXTENSIONS
More terms from Michel Marcus, Oct 11 2013
STATUS
approved