A071875 Decimal expansion of the eighth (of 10) decimal selvage number; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,1

Comments

In other words, this constant satisfies x = Sum_{n>=0} ( floor(10*n*x) (mod 10) ) / 10^n.

The eighth selvage number is equal to the complement of the third selvage number (A071791): s_8 = 1 - s_3.

Links

Table of n, a(n) for n=0..99.

MathWorld, Equidistributed Sequence

Formula

a(n) = floor[10*(n*x)] (Mod 10), where x = sum{k=1..inf} a(k)/10^k.

a(n) = 9 - A071791(n).

Example

x=0.74297429641964186318630853085207520742974296419641...
a(7) = 2 since floor(10*(7*x)) (Mod 10) = 2.
The multiples of this constant x begin:
1*x = 0.7429742964196418631863085308520752074297...
2*x = 1.485948592839283726372617061704150414859...
3*x = 2.228922889258925589558925592556225622289...
4*x = 2.971897185678567452745234123408300829719...
5*x = 3.714871482098209315931542654260376037149...
6*x = 4.457845778517851179117851185112451244578...
7*x = 5.200820074937493042304159715964526452008...
8*x = 5.943794371357134905490468246816601659438...
9*x = 6.686768667776776768676776777668676866868...
10*x = 7.429742964196418631863085308520752074297...
11*x = 8.172717260616060495049393839372827281727...
12*x = 8.915691557035702358235702370224902489157...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

k = 7; f[x_] := Floor[10*FractionalPart[x]]; Clear[xx]; xx[n_] := xx[n] = Catch[ For[x = xx[n - 1], True, x += 10^(-n), If[f[n*x] == f[10^(n - 1)*x], Throw[x]]]]; xx[1] = k/10; Scan[xx, Range[100]]; RealDigits[xx[100]][[1]] (* Jean-François Alcover, Dec 06 2012 *)
Clear[a]; a[1] = 7; a[2] = 4; a[n0=3] = 2; a[_] = 0; digits = 10^(n0-1); Do[a[n] = Mod[Floor[10*n*Sum[a[k]/10^k, {k, 1, n}]], 10], {n, n0+1, digits}]; Table[a[n], {n, 1, digits}] (* Jean-François Alcover, May 12 2015 *)

Crossrefs

Cf. A071789, A071790, A071791, A071792, A071792, A071873, A071874, A071876, A071877.

Sequence in context: A377796 A225410 A248750 * A200687 A200121 A198348

Adjacent sequences: A071872 A071873 A071874 * A071876 A071877 A071878

Keyword

cons,easy,nonn,base

Author

Paul D. Hanna, Jun 10 2002

Status

approved