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%I #29 Jan 20 2017 09:43:11
%S 3,7,1,4,8,2,6,9,3,7,0,4,8,2,5,9,3,6,0,4,8,1,5,9,2,6,0,4,7,1,5,8,2,6,
%T 0,3,7,1,4,8,2,6,9,3,7,0,4,8,2,5,9,3,6,0,4,8,1,5,9,2,6,0,4,7,1,5,8,2,
%U 6,0,3,7,1,4,8,2,6,9,3,7,0,4,8,2,5,9,3,6,0,4,8,1,5,9,2,6,0,4,7,1
%N Decimal expansion of the fourth (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 - A071874(n).
%e x = 0.37148269370482593604815926047158260371482693704825...
%e a(5) = 8 since floor(10*5*x) (mod 10) = 8.
%e The multiples of this constant x begin:
%e 1*x = 0.3714826937048259360481592604715826037148...
%e 2*x = 0.7429653874096518720963185209431652074297...
%e 3*x = 1.114448081114477808144477781414747811144...
%e 4*x = 1.485930774819303744192637041886330414859...
%e 5*x = 1.857413468524129680240796302357913018574...
%e 6*x = 2.228896162228955616288955562829495622289...
%e 7*x = 2.600378855933781552337114823301078226004...
%e 8*x = 2.971861549638607488385274083772660829719...
%e 9*x = 3.343344243343433424433433344244243433433...
%e 10*x = 3.714826937048259360481592604715826037148...
%e 11*x = 4.086309630753085296529751865187408640863...
%e 12*x = 4.457792324457911232577911125658991244578...
%e wherein the tenths place of n*x yields the n-th digit of x.
%t k = 3; 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] = 3; a[2] = 7; a[n0 = 3] = 1; 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. A071789, A071790, A071791, A071793, A071873, A071874, A071875, A071876, A071877.
%K nonn,cons,base,nice
%O 0,1
%A _Paul D. Hanna_, Jun 06 2002
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