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%I #25 Jan 20 2017 09:44:15
%S 4,9,4,9,4,9,4,9,4,9,4,9,4,9,4,9,4,9,4,8,3,8,3,8,3,8,3,8,3,8,3,8,3,8,
%T 3,8,3,8,3,7,2,7,2,7,2,7,2,7,2,7,2,7,2,7,2,7,2,7,2,6,1,6,1,6,1,6,1,6,
%U 1,6,1,6,1,6,1,6,1,6,1,5,0,5,0,5,0,5,0,5,0,5,0,5,0,5,0,5,0,5,9,4
%N Decimal expansion of the fifth (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.
%F a(n) = floor(10*n*x) (mod 10), where x = Sum_{k>0} a(k)/10^k.
%F a(n) = 9 - A071873(n).
%e x = .49494949494949494948383838383838383838372727272727...
%e a(5) = 4 since floor(10*5*x) (mod 10) = 4.
%e The multiples of this constant x begin:
%e 1*x = 0.4949494949494949494838383838383838383837...
%e 2*x = 0.9898989898989898989676767676767676767675...
%e 3*x = 1.484848484848484848451515151515151515151...
%e 4*x = 1.979797979797979797935353535353535353535...
%e 5*x = 2.474747474747474747419191919191919191919...
%e 6*x = 2.969696969696969696903030303030303030302...
%e 7*x = 3.464646464646464646386868686868686868686...
%e 8*x = 3.959595959595959595870707070707070707070...
%e 9*x = 4.454545454545454545354545454545454545454...
%e 10*x = 4.949494949494949494838383838383838383837...
%e 11*x = 5.444444444444444444322222222222222222221...
%e 12*x = 5.939393939393939393806060606060606060605...
%e wherein the tenths place of n*x yields the n-th digit of x.
%t k = 4; 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] = 4; a[2] = 9; a[n0 = 3] = 4; 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}]
%Y Cf. A071789, A071790, A071791, A071792, A071873, A071874, A071875, A071876, A071877.
%K nonn,cons,base,nice
%O 0,1
%A _Paul D. Hanna_, Jun 06 2002
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