A124729
Numbers k such that k, k+1, k+2 and k+3 are products of 5 primes.
Original entry on oeis.org
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
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.
Cf.
A124057,
A124728 Numbers n such that n, n+1, n+2 and n+3 are products of exactly 3,4 primes.
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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 *)
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isok(n) = (bigomega(n) == 5) && (bigomega(n+1) == 5) && (bigomega(n+2) == 5) && (bigomega(n+3) == 5); \\ Michel Marcus, Oct 11 2013
A124728
Numbers k such that k, k+1, k+2 and k+3 are products of 4 primes.
Original entry on oeis.org
4023, 7314, 9162, 12122, 12123, 16674, 19434, 19940, 23874, 24723, 29094, 33234, 35124, 35125, 39234, 42182, 42183, 44163, 45175, 46988, 49147, 51793, 52854, 52855, 54584, 54585, 54663, 58375, 63594, 64074, 64075, 64323, 64491, 64712
Offset: 1
4023=3^3*149, 4024=2^3*503, 4025=5^2*7*23, 4026=2*3*11*61 (all products of 4 primes).
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Transpose[Select[Partition[Range[65000],4,1],Union[PrimeOmega[#]] == {4}&]] [[1]] (* Harvey P. Dale, Nov 01 2011 *)
A268588
Numbers n such that n, n + 1, n + 2, n + 3 and n + 4 are products of exactly three primes.
Original entry on oeis.org
602, 2522, 2523, 4202, 4921, 4922, 5034, 5282, 7730, 18241, 18242, 18571, 19129, 21931, 23161, 23305, 25203, 25553, 25554, 27290, 27291, 29233, 30354, 30793, 32035, 33843, 34561, 35714, 36001, 36835, 40313, 40314, 40394, 45265, 55361, 67609, 69667, 70202, 72721
Offset: 1
a(1) = 602: 602 = 2 * 7 * 43; 603 = 3 * 3 * 67; 604 = 2 * 2 * 151; 605 = 5 * 11 * 11; 606 = 2 * 3 * 101 are all products of three primes.
a(4) = 4202 : 4202 = 2 * 11 * 191; 4203 = 3 * 3 * 467; 4204 = 2 * 2 * 1051; 4205 = 5 * 29 * 29; 4206 = 2 * 3 * 701 are all products of three primes.
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IsP3:=func< n | &+[k[2]: k in Factorization(n)] eq 3 >; [ n: n in [2..50000] | IsP3(n) and IsP3(n+1) and IsP3(n+2) and IsP3(n+3) and IsP3(n+4)];
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with(numtheory): A268588:= proc() if bigomega(n)=3 and bigomega(n+1)=3 and bigomega(n+2)=3 and bigomega(n+3)=3 and bigomega(n+4)=3 then RETURN (n); fi; end: seq(A268588(), n=1..100000);
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Select[Range[100000], PrimeOmega[#] == 3 && PrimeOmega[# + 1] == 3 && PrimeOmega[# + 2] == 3 && PrimeOmega[# + 3] == 3 && PrimeOmega[# + 4] == 3 &]
SequencePosition[PrimeOmega[Range[73000]],{3,3,3,3,3}][[All,1]] (* Harvey P. Dale, Sep 03 2021 *)
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for(n = 1,50000, bigomega(n)==3 & bigomega(n+1)==3 & bigomega(n+2)==3 & bigomega(n+3)==3 & bigomega(n+4)==3 & print1(n,","))
Showing 1-3 of 3 results.
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