A136640 A limited integer Devil's staircase from a winding number function.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 9, 13, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 34, 36, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 51, 53, 54, 56, 58, 58, 60, 61, 63, 65, 67, 67, 67, 67, 67, 67, 70, 72, 73, 75, 76, 77, 79

Offset

1,33

Comments

Designed to be integer and 200 in length, this function is a limited representation of a Devil's staircase function; a projection of a set of rational numbers onto the integers.

Links

Table of n, a(n) for n=1..81.

Per Bak, Commensurate phases, incommensurate phases and the devil's staircase, Rep. Prog. Phys. 45 (1982) pp.587-629.

Eric Weisstein's World of Mathematics, Devil's Staircase.

Formula

a(n) = floor(1+200*Winding_Number(Omega)): 0<=omega<=1;in steps of 1/200

Mathematica

f[{omega_, t_}]:={omega, t+omega-Sin[2Pi t]/(2Pi)}; WindingNumber[n_, {omega_, t_}]:=(Nest[f, {omega, t}, n][[2]]-t)/n; a=Table[Floor[1+200*WindingNumber[1000, {omega, 0}]], {omega, 0, 1, .005}]

Crossrefs

Sequence in context: A312873 A312874 A312875 * A068949 A312876 A312877

Adjacent sequences: A136637 A136638 A136639 * A136641 A136642 A136643

Keyword

nonn,less,uned

Author

Roger L. Bagula, Apr 01 2008

Status

approved