A076433 Perfect powers for which the two closest perfect powers are greater.
25, 121, 2187, 6431296, 6434856, 6956883693, 27027009001, 34359738368, 42618264157, 312078649600, 312079600999, 328080365089, 11305780833649, 11305786504384, 19287643015432, 62854896459664, 79723523012809
Offset: 1
Keywords
Examples
The two closest perfect powers to 25 are 27 (difference = 2) and 32 (difference = 7). The third closest is 16 (difference = 9). Both 27 and 32 are greater than 25, so 25 is in the list.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..22
Programs
-
Python
from itertools import count, islice from sympy import mobius, integer_nthroot def A076433_gen(): # generator of terms def f(x): return int(x+sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length()))) 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 a = bisection(f) b = bisection(lambda x:f(x)+1,a,a) c = bisection(lambda x:f(x)+2,b,b) for i in count(3): d = bisection(lambda x:f(x)+i,c,c) if b-a > d-b: yield b a,b,c=b,c,d A076433_list = list(islice(A076433_gen(),5)) # Chai Wah Wu, Sep 09 2024
Extensions
More terms from Jud McCranie and Robert G. Wilson v, Oct 11 2002
a(6)-a(17) from Donovan Johnson, Sep 03 2008