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

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

Author

Dwight Boddorf, Aug 23 2025

Keywords

• nonn
• new

Comments

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

Links

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

Crossrefs

Cf. A381767, A382131.

Programs

Mathematica

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 *)

Extensions

More terms from Hugo Pfoertner, Aug 23 2025