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A063009
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Write n in binary then square as if written in base 10.
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3
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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; internal format)
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OFFSET
| 0,3
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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 (njas(AT)research.att.com), May 21, 2002
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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.
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FORMULA
| a(2n)=100*a(n); a(2n+1)=100*a(n)+20*A007088(n)+1.
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EXAMPLE
| a(11)=1022121 since 11 written in binary is 1011 and 1011^2=1011000+0+10110+1011=1022121. a(1023) = 1111111111^2 = 1234567900987654321.
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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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 15 2009]
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CROSSREFS
| Cf. A007088 for binary numbers, A001737 for binary squares (post-carry), A063010 for carryless binary squares.
Sequence in context: A143919 A071987 A095633 * A066139 A037139 A109881
Adjacent sequences: A063006 A063007 A063008 * A063010 A063011 A063012
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 04 2001
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