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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 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

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

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Last modified February 25 04:05 EST 2018. Contains 299630 sequences. (Running on oeis4.)