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A048819 Decimal expansion of one of four fixed points (mod 1) of Minkowski's question mark function. 2
4, 2, 0, 3, 7, 2, 3, 3, 9, 4, 2, 3, 2, 2, 3, 0, 7, 5, 6, 4, 0, 9, 9, 3, 0, 0, 6, 6, 4, 6, 2, 2, 1, 8, 7, 3, 9, 4, 9, 1, 8, 9, 8, 6, 6, 6, 0, 0, 6, 1, 1, 8, 7, 1, 2, 9, 1, 6, 5, 4, 6, 6, 4, 6, 8, 6, 5, 5, 3, 3, 7, 0, 8, 8, 5, 9, 7, 9, 0, 8, 0, 3, 5, 5, 7, 4, 3, 9, 0, 5, 6, 0, 3, 9, 2, 8, 3, 3, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Other fixed points (mod 1) are 0, 1/2 and 1-A048819. - Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 10 2006

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 6.9 Minkowski-Bower constant, pp. 441-443.

LINKS

Table of n, a(n) for n=0..98.

Jean-François Alcover, Graph of the question mark function.

S. R. Finch, Minkowski's Question Mark Function

Index entries for sequences related to Minkowski's question mark function

EXAMPLE

0.4203723394232230756409930066462218739491898666...

MATHEMATICA

digits = 99; n0 = 3; dx = 10^-n0; qm[x_] := (ac = Accumulate[ContinuedFraction[x, 200]]; 2 + 2*Sum[(-1)^n* 2^(-ac[[n]]), {n, 1, Length[ac]}]); x = dx; While[N[qm[x], digits+5] < x, x = x + dx]; x0 = x - dx; Do[dx = 10^-n; x = x0; While[N[qm[x], digits+5] < x, x = N[x + dx, digits+5]]; x0 = x - dx , {n, n0+1, digits}]; RealDigits[x0, 10, digits] // First (* Jean-François Alcover, Oct 13 2014 *)

CROSSREFS

Cf. A048817-A048822.

Sequence in context: A176066 A104689 A182501 * A076114 A051478 A121829

Adjacent sequences:  A048816 A048817 A048818 * A048820 A048821 A048822

KEYWORD

nonn,cons

AUTHOR

Christian G. Bower, Apr 15 1999

STATUS

approved

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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.