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A224920 Fifth powers expressed in base 3. 0
1, 1012, 100000, 1101221, 11021202, 101200000, 212001111, 1122221122, 10000000000, 12002011201, 22011220212, 110122100000, 200212022121, 1000022202102, 1102120200000, 1222021101011, 2200010200022, 10120000000000, 11122210120101, 20000120120112 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A223077 A206191 A249987 * A022054 A107518 A073144
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Apr 19 2013
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)