A365887 Numbers k such that k and k+1 are both terms of A365886.

80, 567, 728, 1215, 1376, 1863, 2024, 2511, 2672, 3159, 3320, 3807, 3968, 4455, 4616, 5103, 5264, 5751, 5912, 6399, 6560, 7047, 7208, 7695, 7856, 8343, 8504, 8991, 9152, 9639, 9800, 10287, 10448, 10935, 11096, 11583, 11744, 12231, 12392, 12879, 13040, 13527, 13688

Offset

1,1

Comments

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... .

Links

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

Example

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.

Mathematica

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]

Prog

(PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2]; }
lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = is(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }

Crossrefs

Subsequence of A365886.

A365888 is a subsequence.

Sequence in context: A233354 A200432 A233351 * A107624 A068782 A342188

Adjacent sequences: A365884 A365885 A365886 * A365888 A365889 A365890

Keyword

nonn,easy

Author

Amiram Eldar, Sep 22 2023

Status

approved