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%I #11 Oct 07 2019 12:43:16
%S 1,1012,100000,1101221,11021202,101200000,212001111,1122221122,
%T 10000000000,12002011201,22011220212,110122100000,200212022121,
%U 1000022202102,1102120200000,1222021101011,2200010200022,10120000000000,11122210120101,20000120120112
%N Fifth powers expressed in base 3.
%C Singh proves that there is no solution to 3^a + 3^b + 2 = n^5, when the pairs (a; b) are both even, or one is even and the other is odd. And more generally apart from the exception 2^5 = 3^3 + 3^1 + 2, the Diophantine equation 3^a+3^b+2 = n^5, where GCD(n, 3) = 1 and a > b > 0, is insoluble for 2 < n <= 2 + 6*10^6 (see Singh link).
%H Satyanand Singh, <a href="http://arxiv.org/abs/1304.5020">Perfect Powers of Five with Few Ternary Digits</a>, arXiv:1304.5020 [math.NT], 2013.
%t Table[FromDigits[IntegerDigits[n^5, 3]], {n, 25}] (* _T. D. Noe_, Apr 19 2013 *)
%o (PARI) a(n) = fromdigits(digits(n^5, 3), 10); \\ _Michel Marcus_, Oct 07 2019
%Y Cf. A000584, A007089.
%K nonn,base
%O 1,2
%A _Michel Marcus_, Apr 19 2013