A071791 Decimal expansion of the third (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x.

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

Offset

0,1

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>0} a(k)/10^k.

a(n) = 9 - A071875(n).

Example

x = .25702570358035813681369146914792479257025703580358...
a(6) = 5 since floor(10*6*x) (mod 10) = 5.
The multiples of this constant x begin:
1*x = 0.2570257035803581368136914691479247925703...
2*x = 0.5140514071607162736273829382958495851405...
3*x = 0.7710771107410744104410744074437743777108...
4*x = 1.028102814321432547254765876591699170281...
5*x = 1.285128517901790684068457345739623962851...
6*x = 1.542154221482148820882148814887548755422...
7*x = 1.799179925062506957695840284035473547992...
8*x = 2.056205628642865094509531753183398340562...
9*x = 2.313231332223223231323223222331323133132...
10*x = 2.570257035803581368136914691479247925703...
11*x = 2.827282739383939504950606160627172718273...
12*x = 3.084308442964297641764297629775097510843...
wherein the tenths place of n*x yields the n-th digit of x.

Mathematica

Clear[a]; a[1] = 2; a[2] = 5; a[n0 = 3] = 7; 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}]

Crossrefs

Cf. A071789, A071790, A071792, A071793, A071873, A071874, A071875, A071876, A071877.

Sequence in context: A009376 A231364 A025123 * A248752 A021393 A181583

Adjacent sequences: A071788 A071789 A071790 * A071792 A071793 A071794

Keyword

nonn,cons,base,nice

Author

Paul D. Hanna, Jun 06 2002

Status

approved