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%I #8 Sep 23 2023 15:01:35
%S 228123,903123,1121875,2253123,2928123,3146875,3821875,4278123,
%T 5846875,6303123,6978123,7196875,7871875,9003123,9221875,9896875,
%U 10353123,11028123,11246875,12378123,13053123,13271875,13946875,14403123,15971875,16428123,17103123,17321875
%N Starts of run of 3 consecutive integers that are terms of A365883.
%C Numbers of the form 4*k+2 are not terms of A365883. Therefore there are no runs of 4 or more consecutive integers.
%C 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.
%C 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).
%H Amiram Eldar, <a href="/A365885/b365885.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t q[n_] := Equal @@ FactorInteger[n][[1]]; Select[8*Range[125000] + 3, AllTrue[# + {0, 1, 2}, q] &]
%o (PARI) is(n) = #Set(factor(n)[1,]) == 1;
%o lista(kmax) = forstep(k = 3, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
%Y Subsequence of A017101, A365883, A365884 and A365891.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Sep 22 2023
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