OFFSET
1,1
COMMENTS
b-file is complete: there are 42 terms. - Michael S. Branicky, Aug 27 2021
REFERENCES
H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4, Baywood NY.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..42 [From the Clifford Pickover link. Conjectured to be the full list of terms.]
Clifford A. Pickover, Extreme Challenges in Mathematics and Morals
PROG
(Python)
def ok(n):
s = str(n)
return len(s) == len(set(s)) and set(s) & set(str(n**3)) == set()
print([k**3 for k in range(7659) if ok(k)]) # Michael S. Branicky, Aug 27 2021
(Python) # version for verifying full sequence
from itertools import permutations
def no_repeated_digits():
for d in range(1, 11):
for p in permutations("0123456789", d):
if p[0] == '0': continue
yield int("".join(p))
def afull():
alst = []
for k in no_repeated_digits():
if set(str(k)) & set(str(k**3)) == set():
alst.append(k**3)
return alst
print(afull()) # Michael S. Branicky, Aug 27 2021
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Lekraj Beedassy, Oct 13 2005
EXTENSIONS
Corrected by N. J. A. Sloane, May 22 2008
STATUS
approved