A004631 Squares written in base 16. (Next term contains a non-decimal character.)

1, 4, 9, 10, 19, 24, 31, 40, 51, 64, 79, 90

Offset

0,2

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

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

(End)

References

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See pages 108 and 300.

Links

Table of n, a(n) for n=0..11.

Example

a(8) = 8 * 8 = decimal 64 = 4 * 16 + 0 = "40".
a(15) = 15 * 15 = decimal 225 = 14 * 16 + 1. Using the digit "e" to represent digit-14, a(15) = "e1".

Mathematica

a004631[n_Integer] := BaseForm[n^2, 16]; a004631/@Range[1024] (* Michael De Vlieger, Nov 12 2014 *)

Crossrefs

Cf. A000290.

Sequence in context: A236748 A102837 A356417 * A316113 A336256 A245096

Adjacent sequences: A004628 A004629 A004630 * A004632 A004633 A004634

Keyword

base,easy,nonn

Author

N. J. A. Sloane

Status

approved