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

Author

Amiram Eldar, Sep 22 2023

Keywords

• nonn
• easy

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... .

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A365886.

A365888 is a subsequence.

Programs

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]

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);}