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Decimal expansion of 1/705.
0

%I #22 Apr 24 2024 08:55:58

%S 0,0,1,4,1,8,4,3,9,7,1,6,3,1,2,0,5,6,7,3,7,5,8,8,6,5,2,4,8,2,2,6,9,5,

%T 0,3,5,4,6,0,9,9,2,9,0,7,8,0,1,4,1,8,4,3,9,7,1,6,3,1,2,0,5,6,7,3,7,5,

%U 8,8,6,5,2,4,8,2,2,6,9,5,0,3,5,4,6,0,9,9,2,9,0,7,8,0,1,4,1,8,4

%N Decimal expansion of 1/705.

%H <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1).

%F From _Chai Wah Wu_, Apr 22 2024: (Start)

%F a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) - a(n-14) + a(n-15) - a(n-16) + a(n-17) - a(n-18) + a(n-19) - a(n-20) + a(n-21) - a(n-22) + a(n-23) - a(n-24) + a(n-25) - a(n-26) + a(n-27) - a(n-28) + a(n-29) - a(n-30) + a(n-31) - a(n-32) + a(n-33) - a(n-34) + a(n-35) - a(n-36) + a(n-37) - a(n-38) + a(n-39) - a(n-40) + a(n-41) - a(n-42) + a(n-43) - a(n-44) + a(n-45) for n > 45.

%F G.f.: x^2*(-8*x^43 + x^42 - x^41 - 8*x^40 + 6*x^39 - 15*x^38 + 6*x^37 - 6*x^36 - 4*x^34 - x^33 - 2*x^32 + 2*x^31 - 7*x^30 - 2*x^29 - 4*x^28 + 2*x^27 - 4*x^26 - 4*x^25 - 2*x^23 - 3*x^22 - 3*x^21 - 5*x^20 - 3*x^19 - 2*x^18 - 5*x^17 + 2*x^16 - 9*x^15 + 3*x^14 - 8*x^13 + 8*x^12 - 10*x^11 + 9*x^10 - 12*x^9 + 6*x^8 - 7*x^7 - 9*x^5 + 6*x^4 - 10*x^3 + 2*x^2 - 3*x - 1)/((x - 1)*(x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

%e 0.0014184397163120567375886524822695...

%t Join[{0,0},RealDigits[1/705,10,120][[1]]] (* or *)

%t PadRight[{0},120,{8,0,1,4,1,8,4,3,9,7,1,6,3,1,2,0,5,6,7,3,7,5,8,8,6,5,2,4,8,2,2,6,9,5,0,3,5,4,6,0,9,9,2,9,0,7}] (* _Harvey P. Dale_, Sep 05 2021 *)

%K nonn,cons,easy

%O 0,4

%A _N. J. A. Sloane_