0,1

a(0)=0; to construct the sequence start with a(1)=1, then concatenate twice and change the last term 1->0 giving 1,1,0. Concatenate those 3 terms twice giving 1,1,0,1,1,0,1,1,0, change the last term 0->1 giving 1,1,0,1,1,0,1,1,1. Concatenate those 9 terms twice and change the last term 1->0 etc. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 09 2003

Bill Gosper, Mar 19 2004: It is probably my fault if this constant is misattributed. It was "computed" circa 1971 by a very simple Life pattern (as a diagonal row of blinkers), an obvious case of the (Thue-Siegel-)Roth criterion for transcendence, since the error after 3^n bits is ~2^-3^(n+1) = O(denominator^-3). I probably should have called it Roth's constant.

a(0) = 0; then fixed point of the morphism 1->110, 0->111, starting with a(1) = 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 21 2004

Characteristic function of A007417, i.e. a(n) = 1 if n is in A007417 and a(n) = 0 otherwise . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 21 2004

Multiplicative with a(3^e) = (e+1)%2, a(p^e) = 1 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 10, 2005.

Joerg Arndt, Fxtbook

Michael Gilleland, Some Self-Similar Integer Sequences

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Thue Constant

a(0)=0; for n>=1, a(n)=sum(k>=0, (-1)^k*(floor(n/3^k)-floor((n-1)/3^k))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 03 2003

a(0)=0, a(3k)=1-a(k); a(3k+1)=a(3k+2)=1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 19 2004

Sum_{k=0..3^n} a(k) = A015518(n+1) = (-1)^n*A014983(n+1). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 31 2004

Nest[ Flatten[ # /. {0 -> {1, 1, 1}, 1 -> {1, 1, 0}}] &, {0}, 5] (from Robert G. Wilson v Mar 09 2005)

(PARI) a(n)=if(n<1, 0, sum(k=0, ceil(log(n)/log(3)), (-1)^k*(floor(n/3^k)-floor((n-1)/3^k))))

Cf. Thue-Morse or parity constant A010060.

Sequence in context: A022928 A000494 A022933 this_sequence A030190 A123506 A051105

Adjacent sequences: A014575 A014576 A014577 this_sequence A014579 A014580 A014581

nonn,cons,mult

Eric Weisstein (eric(AT)weisstein.com)