A395753 Indices k where the ratio A000793(k)/A000793(k-1) reaches a new minimum > 1.

2, 3, 4, 8, 27, 29, 41, 128, 132, 133, 199, 516, 584, 798, 822, 1051, 1614, 2323, 12695, 16757, 116365, 216060, 316451, 445402

Offset

1,1

Comments

The sequence gives the positions k in A000793, which is nondecreasing, where the relative increase of two consecutive, but not equal, terms is smaller than any such increase before it. A395751 and A395752 are the numerator and denominator of the relative increase A000793(k)/A000793(k-1)-1.

a(25) > 10^6.

Links

Table of n, a(n) for n=1..24.

Hugo Pfoertner, Plot of A395751(n)/A395752(n) vs A395753(n).

Example

   i    g=A000793(i)      n   a(n)
   |    |   r=g(i)/g(i-1) |   |  A395751(n)
   |    |   |     r-1     |   |  |   A395752(n)
   0    1
   1    1   1
   2    2   2/1   1/1  -> 1   2  1   1
   3    3   3/2   1/2  -> 2   3  1   2
   4    4   4/3   1/3  -> 3   4  1   3
   5    6   3/2   1/2
   6    6   1
   7   12   2/1   1/1
   8   15   5/4   1/4  -> 4   8  1   4
   9   20   4/3   1/3
  10   30   3/2   1/2
  ...
  26  1260  1
  27  1540 11/9   2/9  -> 5  27  2   9
  28  2310  3/2   1/2
  29  2520 12/11  1/11 -> 6  29  1  11

Crossrefs

Cf. A000793, A395744, A395749, A395750, A395751, A395752.

Sequence in context: A368989 A375007 A128657 * A105421 A388408 A273063

Adjacent sequences: A395750 A395751 A395752 * A395754 A395755 A395756

Keyword

nonn,hard,more

Author

Hugo Pfoertner, May 09 2026

Status

approved