A071874 - OEIS

%I #24 May 13 2015 22:13:01

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

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

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

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

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

%C The seventh selvage number is equal to the complement of the fourth selvage number (A071792): s_7 = 1 - s_4.

%H MathWorld, <a href="http://mathworld.wolfram.com/EquidistributedSequence.html">Equidistributed Sequence</a>

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

%F a(n) = 9 - A071792(n).

%e x=0.62851730629517406395184073952841739628517306295174...

%e a(7) = 3 since floor(10*(7*x)) (Mod 10) = 3.

%e The multiples of this constant x begin:

%e 1*x = 0.6285173062951740639518407395284173962852...

%e 2*x = 1.257034612590348127903681479056834792570...

%e 3*x = 1.885551918885522191855522218585252188856...

%e 4*x = 2.514069225180696255807362958113669585141...

%e 5*x = 3.142586531475870319759203697642086981426...

%e 6*x = 3.771103837771044383711044437170504377711...

%e 7*x = 4.399621144066218447662885176698921773996...

%e 8*x = 5.028138450361392511614725916227339170281...

%e 9*x = 5.656655756656566575566566655755756566567...

%e 10*x = 6.285173062951740639518407395284173962852...

%e 11*x = 6.913690369246914703470248134812591359137...

%e 12*x = 7.542207675542088767422088874341008755422...

%e wherein the tenths place of n*x yields the n-th digit of x.

%t k = 6; 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 *)

%t Clear[a]; a[1] = 6; a[2] = 2; a[n0=3] = 8; 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 *)

%Y Cf. A071789, A071790, A071791, A071792, A071792, A071873, A071875, A071876, A071877.

%K cons,easy,nonn,base

%O 0,1

%A _Paul D. Hanna_, Jun 10 2002