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A365888 Starts of run of 3 consecutive integers that are terms of A365886.

%I A365888 #7 Sep 24 2023 05:48:29
%S A365888 3484375,6640623,13609375,16765623,23734375,26890623,33859375,
%T A365888 37015623,43984375,47140623,54109375,57265623,64234375,67390623,
%U A365888 74359375,77515623,84484375,87640623,94609375,97765623,104734375,107890623,114859375,118015623,124984375,128140623
%N A365888 Starts of run of 3 consecutive integers that are terms of A365886.
%C A365888 Numbers k such that k, k+1 and k+2 are all terms of A365886.
%C A365888 Numbers of the form 4*k+2 are not terms of A365886. Therefore there are no runs of 4 or more consecutive integers. Since the middle integer in each triple is even it must be and divisible by 8, so all the terms of this sequence are of the form 8*k+7.
%C A365888 The numbers of terms not exceeding 10^k, for k = 7, 8, ..., are 2, 20, 198, 1979, 19796, ... . Apparently, the asymptotic density of this sequence exists and equals 1.979...*10^(-7).
%H A365888 Amiram Eldar, <a href="/A365888/b365888.txt">Table of n, a(n) for n = 1..10000</a>
%e A365888 3484375 = 5^6 * 223 is a term since its least prime factor, 5, is smaller than its exponent, 6, the least prime factor of 3484376 = 2^3 * 7 * 43 * 1447, 2, is smaller than its exponent, 3, and the least prime factor of 3484377 = 3^5 * 13 * 1103, 3, is also smaller than its exponent, 5.
%t A365888 q[n_] := Less @@ FactorInteger[n][[1]]; Select[8 * Range[10^6] + 7, AllTrue[# + {0, 1, 2}, q] &]
%o A365888 (PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2];}
%o A365888 lista(kmax) = forstep(k = 7, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
%Y A365888 Subsequence of A004771, A365886 and A365887.
%K A365888 nonn
%O A365888 1,1
%A A365888 _Amiram Eldar_, Sep 22 2023