cp's OEIS Frontend

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

%I A365891 #8 Sep 24 2023 05:48:00
%S A365891 228123,446875,903123,1121875,1240623,2253123,2928123,3146875,3821875,
%T A365891 3940623,4159375,4278123,5846875,6303123,6978123,7196875,7871875,
%U A365891 9003123,9221875,9340623,9896875,10353123,10909375,11028123,11246875,12040623,12259375,12378123,13053123
%N A365891 Starts of run of 3 consecutive integers that are terms of A365889.
%C A365891 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.
%C A365891 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).
%H A365891 Amiram Eldar, <a href="/A365891/b365891.txt">Table of n, a(n) for n = 1..10000</a>
%e A365891 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.
%t A365891 q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[4 * Range[2*10^6] + 3, AllTrue[# + {0, 1, 2}, q] &]
%o A365891 (PARI) is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]);}
%o A365891 lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
%Y A365891 Subsequence of A004767, A365889 and A365890.
%Y A365891 A365885 is a subsequence.
%K A365891 nonn
%O A365891 1,1
%A A365891 _Amiram Eldar_, Sep 22 2023