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A071790 Decimal expansion of the second (of 10) decimal selvage numbers; the n-th digit of a decimal selvage number, x, is equal to the tenths digit of n*x. 9

%I

%S 2,4,7,9,2,4,7,9,2,4,7,9,2,4,7,9,2,4,7,9,2,4,7,9,1,4,6,9,1,4,6,9,1,4,

%T 6,9,1,4,6,9,1,4,6,9,1,4,6,9,1,3,6,8,1,3,6,8,1,3,6,8,1,3,6,8,1,3,6,8,

%U 1,3,6,8,0,3,5,8,0,3,5,8,0,3,5,8,0,3,5,8,0,3,5,8,0,3,5,8,0,2,5,7

%N Decimal expansion of the second (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>0} a(k)/10^k.

%F a(n) = 9 - A071876(n).

%e x=.24792479247924792479247914691469146914691469146913...

%e a(8) = 9 since floor(10*8*x) (mod 10) = 9.

%e The multiples of this constant x begin:

%e 1*x = 0.2479247924792479247924791469146914691469...

%e 2*x = 0.4958495849584958495849582938293829382938...

%e 3*x = 0.7437743774377437743774374407440744074407...

%e 4*x = 0.9916991699169916991699165876587658765877...

%e 5*x = 1.239623962396239623962395734573457345735...

%e 6*x = 1.487548754875487548754874881488148814881...

%e 7*x = 1.735473547354735473547354028402840284028...

%e 8*x = 1.983398339833983398339833175317531753175...

%e 9*x = 2.231323132313231323132312322232223222322...

%e 10*x = 2.479247924792479247924791469146914691469...

%e 11*x = 2.727172717271727172717270616061606160616...

%e 12*x = 2.975097509750975097509749762976297629763...

%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] = 2/10; Scan[xx, Range[100]]; RealDigits[xx[100]][[1]] (* _Jean-Fran├žois Alcover_, Nov 30 2012 *)

%t Clear[a]; a[1] = 2; a[2] = 4; a[n0 = 3] = 7; 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-Fran├žois Alcover_, May 11 2015 *)

%Y Cf. A071789, A071791, A071792, 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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Last modified April 21 03:47 EDT 2021. Contains 343145 sequences. (Running on oeis4.)