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

Author

Amiram Eldar, Sep 22 2023

Keywords

• nonn
• easy

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).

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A017101, A365883, A365884 and A365891.

Programs

Mathematica

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

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, ", ")));