A257102 Decimal expansion of A, a constant related to one of Arnold's problems: measuring the randomness of modular arithmetic progressions.

1, 0, 2, 7, 3, 4, 0, 4, 2, 6, 8, 8, 8, 9, 0, 7, 5, 1, 8, 5, 0, 6, 6, 4, 7, 8, 3, 6, 9, 1, 7, 1, 3, 9, 7, 0, 1, 0, 2, 3, 3, 2, 8, 1, 5, 5, 2, 0, 4, 9, 1, 3, 1, 5, 0, 2, 0, 0, 5, 2, 9, 0, 1, 8, 3, 9, 9, 4, 4, 3, 9, 7, 1, 4, 6, 1, 9, 6, 2, 9, 3, 6, 6, 3, 8, 0, 4, 8, 3, 2, 2, 3, 9, 0, 0, 4, 3, 2, 5, 2, 7, 9

Offset

1,3

Links

Table of n, a(n) for n=1..102.

Eda Cesaratto, Alain Plagne and Brigitte Vallée, On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold, Discrete Mathematics and Theoretical Computer Science Proceedings, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006), p. 20.

Formula

A = (1/log(2))*Integral_{1..2} (1/3)*(2/y + 2/y^2 - 1/y^3) + (y-1)*(1/(6*y) + 1/(6*y^2) - 1/(3*y^3)) dy.

A = 2/3 + 1/(4*log(2)).

Example

1.027340426888907518506647836917139701023328155204913150200529...

Mathematica

RealDigits[2/3 + 1/(4*Log[2]), 10, 102] // First

Prog

(PARI) 1/4/log(2)+2/3 \\ Charles R Greathouse IV, Apr 23 2015

Crossrefs

Sequence in context: A248140 A088538 A210516 * A371707 A226626 A249778

Adjacent sequences: A257099 A257100 A257101 * A257103 A257104 A257105

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 23 2015

Status

approved