A365885 Starts of run of 3 consecutive integers that are terms of A365883.

228123, 903123, 1121875, 2253123, 2928123, 3146875, 3821875, 4278123, 5846875, 6303123, 6978123, 7196875, 7871875, 9003123, 9221875, 9896875, 10353123, 11028123, 11246875, 12378123, 13053123, 13271875, 13946875, 14403123, 15971875, 16428123, 17103123, 17321875

Offset

1,1

Comments

Numbers of the form 4*k+2 are not terms of A365883. Therefore there are no runs of 4 or more consecutive integers.

Since the middle integer in each triple is not divisible by 8, all the terms of this sequence are of the form 8*k+3.

The numbers of terms not exceeding 10^k, for k = 6, 7, ..., are 2, 16, 158, 1585, 15853, 158540, ... . Apparently, the asymptotic density of this sequence exists and equals 1.585...*10^(-6).

Links

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

Example

228123 = 3^3 * 7 * 17 * 71 is a term since its least prime factor, 3, is equal to its exponent, the least prime factor of 228123 = 2^2 * 13 * 41 * 107, 2, is equal to its exponent, and the least prime factor of 228125 = 5^5 * 73, 5, is also equal to its exponent.

Mathematica

q[n_] := Equal @@ FactorInteger[n][[1]]; Select[8*Range[125000] + 3, AllTrue[# + {0, 1, 2}, q] &]

Prog

(PARI) is(n) = #Set(factor(n)[1, ]) == 1;
lista(kmax) = forstep(k = 3, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));

Crossrefs

Subsequence of A017101, A365883, A365884 and A365891.

Sequence in context: A287900 A139411 A365891 * A351054 A212727 A234670

Adjacent sequences: A365882 A365883 A365884 * A365886 A365887 A365888

Keyword

nonn,easy

Author

Amiram Eldar, Sep 22 2023

Status

approved