A071876 Decimal expansion of the ninth (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, 5, 2, 0, 7, 5, 2, 0, 7, 5, 2, 0, 7, 5, 2, 0, 7, 5, 2, 0, 7, 5, 2, 0, 8, 5, 3, 0, 8, 5, 3, 0, 8, 5, 3, 0, 8, 5, 3, 0, 8, 5, 3, 0, 8, 5, 3, 0, 8, 6, 3, 1, 8, 6, 3, 1, 8, 6, 3, 1, 8, 6, 3, 1, 8, 6, 3, 1, 8, 6, 3, 1, 9, 6, 4, 1, 9, 6, 4, 1, 9, 6, 4, 1, 9, 6, 4, 1, 9, 6, 4, 1, 9, 6, 4, 1, 9, 7, 4, 2

Offset

0,1

Comments

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

The ninth selvage number is equal to the complement of the second selvage number (A071790): s_9 = 1 - s_2.

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 - A071790(n).

Example

x=0.75207520752075207520752085308530853085308530853086...
a(7) = 2 since floor(10*(7*x)) (Mod 10) = 2.
The multiples of this constant x begin:
1*x = 0.7520752075207520752075208530853085308531...
2*x = 1.504150415041504150415041706170617061706...
3*x = 2.256225622562256225622562559255925592559...
4*x = 3.008300830083008300830083412341234123412...
5*x = 3.760376037603760376037604265426542654265...
6*x = 4.512451245124512451245125118511851185119...
7*x = 5.264526452645264526452645971597159715972...
8*x = 6.016601660166016601660166824682468246825...
9*x = 6.768676867686768676867687677767776777678...
10*x = 7.520752075207520752075208530853085308531...
11*x = 8.272827282728272827282729383938393839384...
12*x = 9.024902490249024902490250237023702370237...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

Clear[a]; a[1] = 7; a[2] = 5; 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, A071875, A071877.

Sequence in context: A272169 A084911 A073742 * A306538 A191503 A318172

Adjacent sequences: A071873 A071874 A071875 * A071877 A071878 A071879

Keyword

cons,easy,nonn,base

Author

Paul D. Hanna, Jun 10 2002

Status

approved