A224920 Fifth powers expressed in base 3.

1, 1012, 100000, 1101221, 11021202, 101200000, 212001111, 1122221122, 10000000000, 12002011201, 22011220212, 110122100000, 200212022121, 1000022202102, 1102120200000, 1222021101011, 2200010200022, 10120000000000, 11122210120101, 20000120120112

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..20.

Satyanand Singh, Perfect Powers of Five with Few Ternary Digits, arXiv:1304.5020 [math.NT], 2013.

Mathematica

Table[FromDigits[IntegerDigits[n^5, 3]], {n, 25}] (* T. D. Noe, Apr 19 2013 *)

Prog

(PARI) a(n) = fromdigits(digits(n^5, 3), 10); \\ Michel Marcus, Oct 07 2019

Crossrefs

Cf. A000584, A007089.

Sequence in context: A223077 A206191 A249987 * A022054 A107518 A073144

Adjacent sequences: A224917 A224918 A224919 * A224921 A224922 A224923

Keyword

nonn,base

Author

Michel Marcus, Apr 19 2013

Status

approved