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Decimal expansion of 1/8991.
3

%I #13 Aug 01 2024 10:32:25

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

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

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

%N Decimal expansion of 1/8991.

%C 1/(89...91) can produce this kind of sequence infinitely.

%D Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See pp. 60, 308.

%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%F sqrt(576576576576576576576576576576576576576576576576576576) = 72*sqrt(111222333444555666777889000111222333444555666777889).

%F G.f.: x^3*(Sum_{i=0..27} floor((i+3)/3)*x^i + x^23 - 9*x^24*(1 + x + x^2 + 10*x^3/9))/(1 - x^27). - _Stefano Spezia_, Jul 31 2024

%e 0.00011122233344455566677788900011...

%t m = 17; Sqrt[Apply[Plus, 576*Table[(10^3)^k, {k, 0, m}]]]

%t Join[{0,0,0},RealDigits[1/8991,10,120][[1]]] (* _Harvey P. Dale_, Apr 22 2012 *)

%Y Cf. A002264, A021895.

%K easy,cons,nonn

%O 0,7

%A Daisuke Minematsu and _Ryohei Miyadera_, Jan 17 2006