|
%I #29 Jan 20 2017 09:39:20
%S 1,2,3,4,6,7,8,9,1,2,3,4,6,7,8,9,0,2,3,4,5,7,8,9,0,2,3,4,5,7,8,9,0,1,
%T 3,4,5,6,8,9,0,1,3,4,5,6,8,9,0,1,2,4,5,6,7,9,0,1,2,4,5,6,7,9,0,1,2,3,
%U 5,6,7,8,0,1,2,3,5,6,7,8,0,1,2,3,4,6,7,8,9,1,2,3,4,6,7,8,9,0,2,3
%N Decimal expansion of the first (of 10) decimal selvage numbers; 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>=1} a(k)/10^k.
%F a(n) = 9 - A071877(n).
%e x=.12346789123467890234578902345789013456890134568901...
%e a(7) = 8 since floor(10*7*x) (mod 10) = 8.
%e The multiples of this constant x begin:
%e 1*x = 0.1234678912346789023457890234578901345689...
%e 2*x = 0.2469357824693578046915780469157802691378...
%e 3*x = 0.3704036737040367070373670703736704037067...
%e 4*x = 0.4938715649387156093831560938315605382756...
%e 5*x = 0.6173394561733945117289451172894506728445...
%e 6*x = 0.7408073474080734140747341407473408074134...
%e 7*x = 0.8642752386427523164205231642052309419823...
%e 8*x = 0.9877431298774312187663121876631210765512...
%e 9*x = 1.111211021112110121112101211121011211120...
%e 10*x = 1.234678912346789023457890234578901345689...
%e 11*x = 1.358146803581467925803679258036791480258...
%e 12*x = 1.481614694816146828149468281494681614827...
%e wherein the tenths place of n*x yields the n-th digit of x.
%t tenth[x_] := Floor[10*FractionalPart[x]]; xx[n_] := xx[n] = Catch[For[x = xx[n-1], True, x += 10^(-n), If[tenth[n*x] == tenth[10^(n-1)*x], Throw[x]]]]; xx[1] = 1/10; Scan[xx, Range[100]]; RealDigits[xx[100]][[1]](* _Jean-François Alcover_, May 10 2012 *)
%t Clear[a]; a[1] = 1; a[2] = 2; a[n0 = 3] = 3; 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 11 2015 *)
%Y Cf. A071790, A071791, A071792, A071793, A071873, A071874, A071875, A071876, A071877.
%K nonn,cons,base,nice
%O 0,2
%A _Paul D. Hanna_, Jun 06 2002
|
