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A112993 Exclusionary cubes: cubes of the terms in A112994.

%I A112993 #17 Aug 27 2021 02:00:20
%S A112993 8,27,343,512,19683,79507,103823,110592,140608,148877,250047,314432,
%T A112993 778688,3869893,5088448,6539203,7077888,18191447,54010152,67917312,
%U A112993 75686967,96071912,102503232,109215352,115501303,146363183,202262003,224755712
%N A112993 Exclusionary cubes: cubes of the terms in A112994.
%C A112993 b-file is complete: there are 42 terms. - _Michael S. Branicky_, Aug 27 2021
%D A112993 H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4, Baywood NY.
%D A112993 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
%H A112993 N. J. A. Sloane, <a href="/A112993/b112993.txt">Table of n, a(n) for n = 1..42</a> [From the Clifford Pickover link. Conjectured to be the full list of terms.]
%H A112993 Clifford A. Pickover, <a href="http://sprott.physics.wisc.edu/Pickover/extremec.html">Extreme Challenges in Mathematics and Morals</a>
%o A112993 (Python)
%o A112993 def ok(n):
%o A112993     s = str(n)
%o A112993     return len(s) == len(set(s)) and set(s) & set(str(n**3)) == set()
%o A112993 print([k**3 for k in range(7659) if ok(k)]) # _Michael S. Branicky_, Aug 27 2021
%o A112993 (Python) # version for verifying full sequence
%o A112993 from itertools import permutations
%o A112993 def no_repeated_digits():
%o A112993     for d in range(1, 11):
%o A112993         for p in permutations("0123456789", d):
%o A112993             if p[0] == '0': continue
%o A112993             yield int("".join(p))
%o A112993 def afull():
%o A112993     alst = []
%o A112993     for k in no_repeated_digits():
%o A112993         if set(str(k)) & set(str(k**3)) == set():
%o A112993             alst.append(k**3)
%o A112993     return alst
%o A112993 print(afull()) # _Michael S. Branicky_, Aug 27 2021
%Y A112993 Cf. A112994.
%K A112993 nonn,base,fini,full
%O A112993 1,1
%A A112993 _Lekraj Beedassy_, Oct 13 2005
%E A112993 Corrected by _N. J. A. Sloane_, May 22 2008