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%I #30 Mar 20 2019 07:22:28
%S 1,27,125,512,1331,3375,753571,2571353,5177717,17173512,25153757,
%T 72511713,11512557512,22211737731,27135225125,125375375125,
%U 552377215125,2252212155712,3531251132352,7127771131125,23771111713777,31122112521375,37521355131352,125112533753375
%N Cubes using only digits 1, 2, 3, 5 and 7.
%C Conjecture: the sequence is finite.
%C Opposite conjecture: the sequence is infinite. The frequency of terms with k digits is 4, 3, 5, 5, 9, 11, 12, 13, 22, 29, 33, 37, 49, 49, 78 for k = 1..15 respectively. - _David A. Corneth_, Mar 17 2019
%H David A. Corneth, <a href="/A074100/b074100.txt">Table of n, a(n) for n = 1..359</a> (Terms < 10^45; first 37 terms from Jayanta Basu)
%e 137^3 = 2571353, smallest term using the five digits 1, 2, 3, 5 and 7. - _Bernard Schott_, Mar 18 2019
%e 91^3 = 753571 as 753571 uses only digits from 1, 2, 3, 5 and 7. It's fine that 91 doesn't. - _David A. Corneth_, Mar 18 2019
%t t1 = Prepend[Prime[Range[4]], 1]; Select[Range[35000]^3, Complement[IntegerDigits[#], t1] == {} &] (* _Jayanta Basu_, Jul 31 2013 *)
%o (Python)
%o A074100_list = [n**3 for n in range(1,10**6) if set(str(n**3)) <= set('12357')] # _Chai Wah Wu_, Mar 16 2019
%Y Cf. A079656.
%K nonn,base
%O 1,2
%A _Amarnath Murthy_, Aug 21 2002
%E More terms from _Sascha Kurz_, Jan 30 2003
%E Two more terms from _Jayanta Basu_, Jul 31 2013
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