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
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Jul 04 2001
STATUS
approved