A071789 Decimal expansion of the first (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,2

Comments

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

Links

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

Formula

a(n) = floor(10*n*x) (mod 10), where x = Sum_{k>=1} a(k)/10^k.

a(n) = 9 - A071877(n).

Example

x=.12346789123467890234578902345789013456890134568901...
a(7) = 8 since floor(10*7*x) (mod 10) = 8.
The multiples of this constant x begin:
1*x = 0.1234678912346789023457890234578901345689...
2*x = 0.2469357824693578046915780469157802691378...
3*x = 0.3704036737040367070373670703736704037067...
4*x = 0.4938715649387156093831560938315605382756...
5*x = 0.6173394561733945117289451172894506728445...
6*x = 0.7408073474080734140747341407473408074134...
7*x = 0.8642752386427523164205231642052309419823...
8*x = 0.9877431298774312187663121876631210765512...
9*x = 1.111211021112110121112101211121011211120...
10*x = 1.234678912346789023457890234578901345689...
11*x = 1.358146803581467925803679258036791480258...
12*x = 1.481614694816146828149468281494681614827...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

tenth[x_] := Floor[10*FractionalPart[x]]; xx[n_] := xx[n] = Catch[For[x = xx[n-1], True, x += 10^(-n), If[tenth[n*x] == tenth[10^(n-1)*x], Throw[x]]]]; xx[1] = 1/10; Scan[xx, Range[100]]; RealDigits[xx[100]][[1]](* Jean-François Alcover, May 10 2012 *)
Clear[a]; a[1] = 1; a[2] = 2; a[n0 = 3] = 3; 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 11 2015 *)

Crossrefs

Cf. A071790, A071791, A071792, A071793, A071873, A071874, A071875, A071876, A071877.

Sequence in context: A086163 A175059 A366429 * A131870 A004724 A099260

Adjacent sequences: A071786 A071787 A071788 * A071790 A071791 A071792

Keyword

nonn,cons,base,nice

Author

Paul D. Hanna, Jun 06 2002

Status

approved