A071876 - OEIS

%I #17 May 13 2015 22:09:03

%S 7,5,2,0,7,5,2,0,7,5,2,0,7,5,2,0,7,5,2,0,7,5,2,0,8,5,3,0,8,5,3,0,8,5,

%T 3,0,8,5,3,0,8,5,3,0,8,5,3,0,8,6,3,1,8,6,3,1,8,6,3,1,8,6,3,1,8,6,3,1,

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

%N Decimal expansion of the ninth (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 ninth selvage number is equal to the complement of the second selvage number (A071790): s_9 = 1 - s_2.

%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 - A071790(n).

%e x=0.75207520752075207520752085308530853085308530853086...

%e a(7) = 2 since floor(10*(7*x)) (Mod 10) = 2.

%e The multiples of this constant x begin:

%e 1*x = 0.7520752075207520752075208530853085308531...

%e 2*x = 1.504150415041504150415041706170617061706...

%e 3*x = 2.256225622562256225622562559255925592559...

%e 4*x = 3.008300830083008300830083412341234123412...

%e 5*x = 3.760376037603760376037604265426542654265...

%e 6*x = 4.512451245124512451245125118511851185119...

%e 7*x = 5.264526452645264526452645971597159715972...

%e 8*x = 6.016601660166016601660166824682468246825...

%e 9*x = 6.768676867686768676867687677767776777678...

%e 10*x = 7.520752075207520752075208530853085308531...

%e 11*x = 8.272827282728272827282729383938393839384...

%e 12*x = 9.024902490249024902490250237023702370237...

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

%t Clear[a]; a[1] = 7; a[2] = 5; 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, A071875, A071877.

%K cons,easy,nonn,base

%O 0,1

%A _Paul D. Hanna_, Jun 10 2002