A365887 - OEIS

%I #8 Sep 24 2023 05:48:16

%S 80,567,728,1215,1376,1863,2024,2511,2672,3159,3320,3807,3968,4455,

%T 4616,5103,5264,5751,5912,6399,6560,7047,7208,7695,7856,8343,8504,

%U 8991,9152,9639,9800,10287,10448,10935,11096,11583,11744,12231,12392,12879,13040,13527,13688

%N Numbers k such that k and k+1 are both terms of A365886.

%C The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 3, 31, 310, 3097, 30971, 309711, 3097110, 30971095, 309710953, ... . Apparently, the asymptotic density of this sequence exists and equals 0.003097109... .

%H Amiram Eldar, <a href="/A365887/b365887.txt">Table of n, a(n) for n = 1..10000</a>

%e 80 = 2^4 * 5 is a term since its least prime factor, 2, is smaller than its exponent, 4, and the least prime factor of 81 = 3^4, 3, is also smaller than its exponent, 4.

%t q[n_] := Less @@ FactorInteger[n][[1]]; consec[kmax_] := Module[{m = 1, c = Table[False, {2}], s = {}}, Do[c = Join[Rest[c], {q[k]}]; If[And @@ c, AppendTo[s, k - 1]], {k, 1, kmax}]; s]; consec[14000]

%o (PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2];}

%o lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = is(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

%Y Subsequence of A365886.

%Y A365888 is a subsequence.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Sep 22 2023