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A365888 Starts of run of 3 consecutive integers that are terms of A365886. 3
3484375, 6640623, 13609375, 16765623, 23734375, 26890623, 33859375, 37015623, 43984375, 47140623, 54109375, 57265623, 64234375, 67390623, 74359375, 77515623, 84484375, 87640623, 94609375, 97765623, 104734375, 107890623, 114859375, 118015623, 124984375, 128140623 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that k, k+1 and k+2 are all terms of A365886.
Numbers of the form 4*k+2 are not terms of A365886. Therefore there are no runs of 4 or more consecutive integers. Since the middle integer in each triple is even it must be and divisible by 8, so all the terms of this sequence are of the form 8*k+7.
The numbers of terms not exceeding 10^k, for k = 7, 8, ..., are 2, 20, 198, 1979, 19796, ... . Apparently, the asymptotic density of this sequence exists and equals 1.979...*10^(-7).
LINKS
EXAMPLE
3484375 = 5^6 * 223 is a term since its least prime factor, 5, is smaller than its exponent, 6, the least prime factor of 3484376 = 2^3 * 7 * 43 * 1447, 2, is smaller than its exponent, 3, and the least prime factor of 3484377 = 3^5 * 13 * 1103, 3, is also smaller than its exponent, 5.
MATHEMATICA
q[n_] := Less @@ FactorInteger[n][[1]]; Select[8 * Range[10^6] + 7, AllTrue[# + {0, 1, 2}, q] &]
PROG
(PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2]; }
lista(kmax) = forstep(k = 7, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
CROSSREFS
Subsequence of A004771, A365886 and A365887.
Sequence in context: A206107 A349065 A204335 * A240105 A205766 A183790
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved

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Last modified July 15 14:56 EDT 2024. Contains 374333 sequences. (Running on oeis4.)