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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 (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 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 * A184372 A237402 A210106

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

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Last modified June 18 17:32 EDT 2021. Contains 345120 sequences. (Running on oeis4.)