

A063009


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


5



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
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OFFSET

0,3


COMMENTS

The original description was: "Precarry 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=xb*(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


CROSSREFS

Cf. A007088 for binary numbers, A001737 for binary squares (postcarry), A063010 for carryless binary squares.
Sequence in context: A071987 A095633 A228103 * A066139 A037139 A109881
Adjacent sequences: A063006 A063007 A063008 * A063010 A063011 A063012


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, Jul 04 2001


STATUS

approved



