A365888 Starts of run of 3 consecutive integers that are terms of A365886.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A365885 A365886 A365887 * A365889 A365890 A365891

Keyword

nonn

Author

Amiram Eldar, Sep 22 2023

Status

approved