A269023 - OEIS

A269023

Complement of A269020: numbers not of the form ceiling(n^(1+1/n)).

2, 4, 8, 19, 51, 141, 392, 1079, 2957, 8072, 21987, 59825, 162695, 442342, 1202521, 3268920, 8885999, 24154826, 65659826, 178482140

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OFFSET

1,1

COMMENTS

The limiting ratio is e (see comment in A059921).

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

The term 8 appears because A269020(5)=7 and A269020(6)=9.

MATHEMATICA

Complement[Range[1, 100000], Table[Ceiling[n^(1 + 1/n)], {n, 100000}]] (* Vaclav Kotesovec, Mar 12 2016 *)

PROG

(PARI) a269020(n) = ceil(n^(1+1/n))

for(n=1, 1e20, if(a269020(n+1)-a269020(n) > 1, print1(a269020(n)+1, ", "))) \\ Felix Fröhlich, Mar 12 2016

(Python)

from itertools import count

def A269023(n):

def bisection(f, kmin=0, kmax=1):

while f(kmax) > kmax: kmax <<= 1

while kmax-kmin > 1:

kmid = kmax+kmin>>1

if f(kmid) <= kmid:

kmax = kmid

else:

kmin = kmid

return kmax

def f(x):

if x==1: return n+1

z = x**x

for y in count(x, -1):

if y**(y+1) <= z:

return n+y

z //= x

return bisection(f, n, n) # Chai Wah Wu, Sep 10 2024

CROSSREFS

Cf. A059921, A269020.

Sequence in context: A003081 A100133 A099598 * A173310 A320178 A128816

Adjacent sequences: A269020 A269021 A269022 * A269024 A269025 A269026

KEYWORD

nonn,more

AUTHOR

Bob Selcoe, Feb 18 2016

EXTENSIONS

a(18)-a(20) from Felix Fröhlich, Mar 12 2016

STATUS

approved