A381767 -id:A381767 - cp's OEIS frontend

A382131 Complement of A381767.

2, 3, 5, 15, 46, 136, 385, 1072, 2949, 8063, 21977, 59814, 162683, 442329, 1202507, 3268905, 8885983, 24154809, 65659808, 178482121, 485164996, 1318815514, 3584912605, 9744803182, 26489121842, 72004899025, 195729609091, 532048240238, 1446257063900, 3931334296724, 10686474581075

Offset: 1

Mike Sheppard, Mar 16 2025

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..100

Cf. A381767.

a(n) ~ e^(n-1) (conjectured)

e^(n-1) - 2*n^2 < a(n) < e^(n-1). - Yifan Xie, May 20 2025

More terms from David A. Corneth, May 20 2025

A387243 a(n) is the smallest positive k such that (k+n)^k < (k+1)^(k+1).

Original entry on oeis.org

1, 1, 2, 11, 41, 130, 378, 1064, 2940, 8053, 21966, 59802, 162670, 442315, 1202492, 3268889, 8885966, 24154791, 65659789, 178482101, 485164975, 1318815492, 3584912582, 9744803158, 26489121817, 72004898999, 195729609064, 532048240210, 1446257063871, 3931334296694

Offset: 1

Dwight Boddorf, Aug 23 2025

Conjecture: a(n) = A382131(n) - n.

Chai Wah Wu, Table of n, a(n) for n = 1..500

Cf. A381767, A382131.

a[n_]:=Floor[NSolveValues[k*Log[(k+n)]==(k+1)*Log[(k+1)], k, Reals]][[-1]]+1; Array[a, 30] (* James C. McMahon, Aug 31 2025 *)

More terms from Hugo Pfoertner, Aug 23 2025

cp's OEIS Frontend

A382131 Complement of A381767.

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