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%I #20 May 13 2015 22:10:08
%S 8,7,6,5,3,2,1,0,8,7,6,5,3,2,1,0,9,7,6,5,4,2,1,0,9,7,6,5,4,2,1,0,9,8,
%T 6,5,4,3,1,0,9,8,6,5,4,3,1,0,9,8,7,5,4,3,2,0,9,8,7,5,4,3,2,0,9,8,7,6,
%U 4,3,2,1,9,8,7,6,4,3,2,1,9,8,7,6,5,3,2,1,0,8,7,6,5,3,2,1,0,9,7,6
%N Decimal expansion of the tenth (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 tenth selvage number is equal to the complement of the first selvage number (A071789): s_10 = 1 - s_1.
%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 - A071789(n).
%e x=0.87653210876532109765421097654210986543109865431098...
%e a(7) = 1 since floor(10*(7*x)) (Mod 10) = 1.
%e The multiples of this constant x begin:
%e 1*x = 0.8765321087653210976542109765421098654311...
%e 2*x = 1.753064217530642195308421953084219730862...
%e 3*x = 2.629596326295963292962632929626329596293...
%e 4*x = 3.506128435061284390616843906168439461724...
%e 5*x = 4.382660543826605488271054882710549327155...
%e 6*x = 5.259192652591926585925265859252659192587...
%e 7*x = 6.135724761357247683579476835794769058018...
%e 8*x = 7.012256870122568781233687812336878923449...
%e 9*x = 7.888788978887889878887898788878988788880...
%e 10*x = 8.765321087653210976542109765421098654311...
%e 11*x = 9.641853196418532074196320741963208519742...
%e 12*x = 10.51838530518385317185053171850531838517...
%e wherein the tenths place of n*x yields the n-th digit of x.
%t k = 8; 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] = 8; a[2] = 7; a[n0=3] = 6; 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, A071875, A071876.
%K cons,easy,nonn,base
%O 0,1
%A _Paul D. Hanna_, Jun 10 2002
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