This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269023 #22 Sep 10 2024 20:20:43
%S A269023 2,4,8,19,51,141,392,1079,2957,8072,21987,59825,162695,442342,1202521,
%T A269023 3268920,8885999,24154826,65659826,178482140
%N A269023 Complement of A269020: numbers not of the form ceiling(n^(1+1/n)).
%C A269023 The limiting ratio is e (see comment in A059921).
%e A269023 The term 8 appears because A269020(5)=7 and A269020(6)=9.
%t A269023 Complement[Range[1, 100000], Table[Ceiling[n^(1 + 1/n)], {n, 100000}]] (* _Vaclav Kotesovec_, Mar 12 2016 *)
%o A269023 (PARI) a269020(n) = ceil(n^(1+1/n))
%o A269023 for(n=1, 1e20, if(a269020(n+1)-a269020(n) > 1, print1(a269020(n)+1, ", "))) \\ _Felix Fröhlich_, Mar 12 2016
%o A269023 (Python)
%o A269023 from itertools import count
%o A269023 def A269023(n):
%o A269023 def bisection(f,kmin=0,kmax=1):
%o A269023 while f(kmax) > kmax: kmax <<= 1
%o A269023 while kmax-kmin > 1:
%o A269023 kmid = kmax+kmin>>1
%o A269023 if f(kmid) <= kmid:
%o A269023 kmax = kmid
%o A269023 else:
%o A269023 kmin = kmid
%o A269023 return kmax
%o A269023 def f(x):
%o A269023 if x==1: return n+1
%o A269023 z = x**x
%o A269023 for y in count(x,-1):
%o A269023 if y**(y+1) <= z:
%o A269023 return n+y
%o A269023 z //= x
%o A269023 return bisection(f,n,n) # _Chai Wah Wu_, Sep 10 2024
%Y A269023 Cf. A059921, A269020.
%K A269023 nonn,more
%O A269023 1,1
%A A269023 _Bob Selcoe_, Feb 18 2016
%E A269023 a(18)-a(20) from _Felix Fröhlich_, Mar 12 2016