A257283 Numbers n not divisible by 3 such that n^2 written in base 3 has no digit > 1.

1, 2, 11, 16, 19, 29, 55, 83, 143, 163, 245, 262, 421, 451, 487, 731, 889, 1331, 1342, 1459, 1487, 2189, 2242, 2323, 2537, 2573, 2644, 2662, 3788, 4375, 4562, 6563, 6688, 6967, 7036, 7082, 7696, 8035

Offset

1,2

Comments

The first condition is added to avoid trivial solutions of the form a(k)*3^m, whose square, written in base 3, would just have 0's appended w.r.t. a(k)^2, and thus always have the digits 1 and 0.

An infinite subset of solutions is given by { 3^m+2; m>1 } U { 2*3^m+1; m>1 }.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..200

Mathematica

Select[Range[10000], Mod[#, 3]!=0&&Max[IntegerDigits[#^2, 3]]<2&] (* Harvey P. Dale, May 17 2018 *)

Prog

(PARI) b=3; for(n=1, 9999, n%b||next; vecmax(digits(n^2, b))>1||print1(n", "))

Crossrefs

Cf. A257284, A230030.

Sequence in context: A241757 A377473 A272883 * A091211 A306278 A199397

Adjacent sequences: A257280 A257281 A257282 * A257284 A257285 A257286

Keyword

nonn,base

Author

M. F. Hasler, May 02 2015

Status

approved