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A365884
Numbers k such that k and k+1 are both terms of A365883.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved