A063009 Write n in binary then square as if written in base 10.

0, 1, 100, 121, 10000, 10201, 12100, 12321, 1000000, 1002001, 1020100, 1022121, 1210000, 1212201, 1232100, 1234321, 100000000, 100020001, 100200100, 100220121, 102010000, 102030201, 102212100, 102232321, 121000000, 121022001

Offset: 0

Author

Henry Bottomley, Jul 04 2001

Keywords

• base
• easy
• nonn

Comments

The original description was: "Pre-carry binary squares: write n in binary then square as if written in a base large enough to avoid carries". But I changed it, since I prefer to work in base 10. There is no difference until a(1023). - N. J. A. Sloane, May 21 2002

Examples

			a(11)=1022121 since 11 written in binary is 1011 and 1011^2 = 1011000 + 0 + 10110 + 1011 = 1022121.
a(1023) = 1111111111^2 = 1234567900987654321.
		

Links

• Harry J. Smith, Table of n, a(n) for n=0,...,1000
• David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.

Crossrefs

Cf. A007088 for binary numbers, A001737 for binary squares (post-carry), A063010 for carryless binary squares.

Programs

PARI

a(n) = fromdigits(binary(n))^2; \\ Ruud H.G. van Tol, Dec 08 2022

Formula

a(2n) = 100*a(n); a(2n+1) = 100*a(n) + 20*A007088(n) + 1.