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A365871
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Starts of runs of 3 consecutive integers whose exponent of least prime factor in their prime factorization is even.
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3
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475, 1519, 2223, 2275, 3283, 4475, 4923, 4975, 5823, 6723, 6811, 7299, 7675, 8107, 8379, 8523, 8955, 9475, 10323, 10467, 11275, 12427, 12463, 12591, 13075, 13867, 13923, 14355, 15631, 15723, 16675, 18027, 18275, 18475, 18767, 19323, 19375, 19647, 22075, 22831
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OFFSET
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1,1
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COMMENTS
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Numbers k such that k, k+1 and k+2 are all terms of A365869.
Numbers of the form 4*k+2 are not terms of A365869. Therefore, there are no runs of 4 or more consecutive integers, and all the terms of this sequence are of the form 4*k+3.
The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 1, 18, 195, 1952, 19542, 195514, 1955859, 19560453, 195611458, ... . Apparently, the asymptotic density of this sequence exists and equals 0.001956... .
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LINKS
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EXAMPLE
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475 is a term since the exponent of the prime factor 5 in the factorization 475 = 5^2 * 19 is 2, which is even, the exponent of the prime factor 2 in the factorization 476 = 2^2 * 7 * 17 is 2, which is even, and the exponent of the prime factor 3 in the factorization 477 = 3^2 * 53 is also 2, which is even.
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MATHEMATICA
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Select[4 * Range[6000] + 3, AllTrue[# + {0, 1, 2}, EvenQ[FactorInteger[#1][[1, -1]]] &] &]
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PROG
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(PARI) is(n) = !(factor(n)[1, 2]%2);
lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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