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

0,3

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

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.

Formula

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

Example

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

Prog

(PARI) baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { for (n=0, 1000, write("b063009.txt", n, " ", baseE(n, 2)^2) ) } \\ Harry J. Smith, Aug 15 2009
(PARI) a(n) = fromdigits(binary(n))^2; \\ Ruud H.G. van Tol, Dec 08 2022

Crossrefs

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

Sequence in context: A095633 A228103 A331543 * A066139 A109881 A292275

Adjacent sequences: A063006 A063007 A063008 * A063010 A063011 A063012

Keyword

base,easy,nonn

Author

Henry Bottomley, Jul 04 2001

Status

approved