A365891 Starts of run of 3 consecutive integers that are terms of A365889.

228123, 446875, 903123, 1121875, 1240623, 2253123, 2928123, 3146875, 3821875, 3940623, 4159375, 4278123, 5846875, 6303123, 6978123, 7196875, 7871875, 9003123, 9221875, 9340623, 9896875, 10353123, 10909375, 11028123, 11246875, 12040623, 12259375, 12378123, 13053123

Offset

1,1

Comments

Numbers of the form 4*k+2 are not terms of A365889. 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 = 6, 7, ..., are 3, 21, 220, 2193, 21954, 219583, ... . Apparently, the asymptotic density of this sequence exists and equals 2.195...*10^(-6).

Links

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

Example

446875 = 5^5 * 11 * 13 is a term since its least prime factor, 5, divides it exponent, 5, the least prime factor of 446876 = 2^2 * 47 * 2377, 2, divides its exponent, 2, and the least prime factor of 446877 = 3^6 * 613, 3, also divides its exponent, 6.

Mathematica

q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[4 * Range[2*10^6] + 3, AllTrue[# + {0, 1, 2}, q] &]

Prog

(PARI) is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]); }
lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));

Crossrefs

Subsequence of A004767, A365889 and A365890.

A365885 is a subsequence.

Sequence in context: A179730 A287900 A139411 * A365885 A351054 A212727

Adjacent sequences: A365888 A365889 A365890 * A365892 A365893 A365894

Keyword

nonn

Author

Amiram Eldar, Sep 22 2023

Status

approved