A201918 Automorphic numbers: n^2 ends with n in base 12 (written in base 10).

0, 1, 4, 9, 64, 81, 513, 1216, 6400, 14337, 234496, 483328, 2502657, 17432577, 18399232, 412549120, 842530816, 4317249537, 11162091520, 50755272705, 692253097984, 2178269839360, 6737830608897, 46758772080640, 60234433298433, 474731593596928, 809186870951937

Offset: 1

Author

Martin Renner, Dec 06 2011

Keywords

• nonn
• base

Examples

			a(3) = 4 = (4)_12 since 4^2 = 16 = (14)_12 ends with 4 in base 12.
a(4) = 9 = (9)_12 since 9^2 = 81 = (69)_12 ends with 9 in base 12.
a(5) = 64 = (54)_12 since 64^2 = 4096 = (2454)_12 ends with 54 in base 12.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003226, A201821, A201919, A201921, A201948, A237583.

Programs

Mathematica

a201918[n_Integer] := Module[{i = 0}, Flatten[Last[Reap[
     Do[If[
       IntegerDigits[i^2, 12][[-Length[IntegerDigits[i, 12]] ;; -1]] ==
         IntegerDigits[i, 12], Sow[i]], {i, n}]]]]]; a201918[12^6] (* Michael De Vlieger, Aug 13 2014 *)

Sage

# See A003226. - Eric M. Schmidt, Feb 09 2014

Extensions

More terms from Eric M. Schmidt, Feb 09 2014