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A112994 Numbers whose cubes are exclusionary: numbers k such that k has no repeated digits and k and k^3 have no digits in common.

%I A112994 #22 Sep 06 2021 19:00:37
%S A112994 2,3,7,8,27,43,47,48,52,53,63,68,92,157,172,187,192,263,378,408,423,
%T A112994 458,468,478,487,527,587,608,648,692,823,843,918,1457,1587,1592,4657,
%U A112994 4732,5692,6058,6378,7658
%N A112994 Numbers whose cubes are exclusionary: numbers k such that k has no repeated digits and k and k^3 have no digits in common.
%C A112994 A number k with no repeated digits has an exclusionary cube k^3 if the latter is made up of digits not appearing in k. (This is a subsequence of A029785.) For the corresponding exclusionary cubes see A112993. Conjectured to be complete.
%C A112994 Data are complete: there are 42 terms. - _Michael S. Branicky_, Aug 27 2021
%D A112994 H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, vol. 32 No.4 2003-4, Baywood NY.
%D A112994 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
%H A112994 Clifford A. Pickover, <a href="http://sprott.physics.wisc.edu/Pickover/extremec.html">Extreme Challenges in Mathematics and Morals</a>
%t A112994 Select[Range[8000],Max[DigitCount[#]]==1&&Intersection[IntegerDigits[ #],IntegerDigits[#^3]]=={}&] (* _Harvey P. Dale_, Sep 06 2021 *)
%o A112994 (PARI) isok(n) = my(digs = digits(n)); (#digs == #Set(digs)) && (#setintersect(Set(digs), Set(digits(n^3))) == 0); \\ _Michel Marcus_, Oct 26 2013
%o A112994 (Python)
%o A112994 def ok(n):
%o A112994     s = str(n)
%o A112994     return len(s) == len(set(s)) and set(s) & set(str(n**3)) == set()
%o A112994 print([k for k in range(7659) if ok(k)]) # _Michael S. Branicky_, Aug 27 2021
%o A112994 (Python) # version for verifying full sequence
%o A112994 from itertools import permutations
%o A112994 def no_repeated_digits():
%o A112994     for d in range(1, 11):
%o A112994         for p in permutations("0123456789", d):
%o A112994             if p[0] == '0': continue
%o A112994             yield int("".join(p))
%o A112994 def afull():
%o A112994     alst = []
%o A112994     for k in no_repeated_digits():
%o A112994         if set(str(k)) & set(str(k**3)) == set():
%o A112994             alst.append(k)
%o A112994     return alst
%o A112994 print(afull()) # _Michael S. Branicky_, Aug 27 2021
%Y A112994 Subsequence of A029785.
%Y A112994 The corresponding cubes are in A112993.
%K A112994 nonn,base,fini,full
%O A112994 1,1
%A A112994 _Lekraj Beedassy_, Oct 13 2005
%E A112994 Missing term 468 added by _N. J. A. Sloane_, May 22 2008
%E A112994 Definition clarified by _Harvey P. Dale_, Sep 06 2021