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%I #20 May 13 2015 22:07:02
%S 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,
%T 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,
%U 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
%N 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.
%C In other words, this constant satisfies x = Sum_{n>=0} ( floor(10*n*x) (mod 10) ) / 10^n.
%C The eighth selvage number is equal to the complement of the third selvage number (A071791): s_8 = 1 - s_3.
%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 - A071791(n).
%e x=0.74297429641964186318630853085207520742974296419641...
%e a(7) = 2 since floor(10*(7*x)) (Mod 10) = 2.
%e The multiples of this constant x begin:
%e 1*x = 0.7429742964196418631863085308520752074297...
%e 2*x = 1.485948592839283726372617061704150414859...
%e 3*x = 2.228922889258925589558925592556225622289...
%e 4*x = 2.971897185678567452745234123408300829719...
%e 5*x = 3.714871482098209315931542654260376037149...
%e 6*x = 4.457845778517851179117851185112451244578...
%e 7*x = 5.200820074937493042304159715964526452008...
%e 8*x = 5.943794371357134905490468246816601659438...
%e 9*x = 6.686768667776776768676776777668676866868...
%e 10*x = 7.429742964196418631863085308520752074297...
%e 11*x = 8.172717260616060495049393839372827281727...
%e 12*x = 8.915691557035702358235702370224902489157...
%e wherein the tenths place of n*x yields the n-th digit of x.
%t 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 *)
%t 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 *)
%Y Cf. A071789, A071790, A071791, A071792, A071792, A071873, A071874, A071876, A071877.
%K cons,easy,nonn,base
%O 0,1
%A _Paul D. Hanna_, Jun 10 2002
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