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A365887
Numbers k such that k and k+1 are both terms of A365886.
3
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
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 A388001 A389955
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved