A365884 Numbers k such that k and k+1 are both terms of A365883.

27, 188, 459, 620, 675, 836, 1107, 1268, 1323, 1484, 1755, 1916, 1971, 2132, 2403, 2564, 2619, 2780, 3051, 3124, 3212, 3267, 3428, 3699, 3860, 3915, 4076, 4347, 4508, 4563, 4724, 4995, 5156, 5211, 5372, 5643, 5804, 5859, 6020, 6291, 6452, 6507, 6668, 6939, 7100

Offset

1,1

Comments

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 6, 63, 623, 6216, 62157, 621565, 6215645, 62156450, 621564494, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00621564... .

Links

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

Example

27 = 3^3 is a term since its least prime factor, 3, is equal to its exponent, and also the least prime factor of 28 = 2^2 * 7, 2, is equal to its exponent.

Mathematica

q[n_] := Equal @@ 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[7200]

Prog

(PARI) lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = #Set(factor(k)[1, ]) == 1; if(q1 && q2, print1(k-1, ", ")); q1 = q2); }

Crossrefs

Subsequence of A365883 and A365890.

A365885 is a subsequence.

Sequence in context: A228463 A000499 A365890 * A042416 A216108 A216110

Adjacent sequences: A365881 A365882 A365883 * A365885 A365886 A365887

Keyword

nonn,easy

Author

Amiram Eldar, Sep 22 2023

Status

approved