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A063010 Carryless binary square of n; also Moser-de Bruijn sequence written in binary. 3
0, 1, 100, 101, 10000, 10001, 10100, 10101, 1000000, 1000001, 1000100, 1000101, 1010000, 1010001, 1010100, 1010101, 100000000, 100000001, 100000100, 100000101, 100010000, 100010001, 100010100, 100010101, 101000000, 101000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers that are sums of distinct powers of 100. - David Wasserman, Feb 26 2008

LINKS

Table of n, a(n) for n=0..25.

David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version

FORMULA

a(n)=A062033(n)/10 i.e. with final zero removed.

a(n)=Sum_k>=0 {A030308(n,k)*A098608(k)}. - From Philippe Deléham, Oct 15 2011.

G.f.: (1/(1 - x))*Sum_{k>=0} 100^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

EXAMPLE

a(11)=1000101, since 11 in binary is 1011 and binary carryless sum of 1011000, 0, 10110 and 1011 is 1000101.

CROSSREFS

Cf. Moser-de Bruijn sequence A000695, carryless decimal squares A059729, pre-carry binary squares A063009.

Sequence in context: A091254 A085251 A178530 * A215022 A094027 A281149

Adjacent sequences:  A063007 A063008 A063009 * A063011 A063012 A063013

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Jul 03 2001

EXTENSIONS

More terms from David Wasserman, Feb 26 2008

STATUS

approved

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Last modified January 20 10:23 EST 2018. Contains 297960 sequences.