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