A004630 Squares written in base 12. (Next term contains a non-decimal character.)

1, 4, 9, 14, 21, 30, 41, 54, 69, 84

Offset

1,2

Comments

From Michael De Vlieger, Nov 12 2014: (Start)

The next term contains a nondecimal digit: see the link below for an expanded table of squares with the nondecimal digits.

Perfect squares in base 12 must end in one of {0, 1, 4, 9}, similar to perfect squares in base 16.

As n increases, a(n) cycles through the end digits in the order {0, 1, 4, 9, 4, 1}.

(End)

Links

Table of n, a(n) for n=1..10.

Michael De Vlieger, Squares written in base 12, a(n) for n = 1..1728 (duodecimal 1000)

Example

a(8) = 8 * 8 = decimal 64 = 5 dozen 4 = "54".
a(15) = 15 * 15 = decimal 225 = 1 gross 6 dozen 9 (or 1 * (12^2) + 6 * (12^1) + 9) = "169".

Mathematica

a004630[n_Integer] := BaseForm[n^2, 12]; a004630/@Range[12^3] (* Michael De Vlieger, Nov 12 2014 *)

Crossrefs

Cf. A000290.

Sequence in context: A115585 A099980 A281314 * A073497 A244941 A086192

Adjacent sequences: A004627 A004628 A004629 * A004631 A004632 A004633

Keyword

base,easy,nonn

Author

N. J. A. Sloane

Status

approved