A395753 - OEIS

%I #9 May 12 2026 16:21:27

%S 2,3,4,8,27,29,41,128,132,133,199,516,584,798,822,1051,1614,2323,

%T 12695,16757,116365,216060,316451,445402

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

%C 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.

%C a(25) > 10^6.

%H Hugo Pfoertner, <a href="/A395753/a395753.png">Plot of A395751(n)/A395752(n) vs A395753(n)</a>.

%e    i    g=A000793(i)      n   a(n)

%e    |    |   r=g(i)/g(i-1) |   |  A395751(n)

%e    |    |   |     r-1     |   |  |   A395752(n)

%e    0    1

%e    1    1   1

%e    2    2   2/1   1/1  -> 1   2  1   1

%e    3    3   3/2   1/2  -> 2   3  1   2

%e    4    4   4/3   1/3  -> 3   4  1   3

%e    5    6   3/2   1/2

%e    6    6   1

%e    7   12   2/1   1/1

%e    8   15   5/4   1/4  -> 4   8  1   4

%e    9   20   4/3   1/3

%e   10   30   3/2   1/2

%e   ...

%e   26  1260  1

%e   27  1540 11/9   2/9  -> 5  27  2   9

%e   28  2310  3/2   1/2

%e   29  2520 12/11  1/11 -> 6  29  1  11

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

%K nonn,hard,more

%O 1,1

%A _Hugo Pfoertner_, May 09 2026