A113675 Decimal expansion of 1/8991.

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, 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, 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

Offset: 0

Author

Daisuke Minematsu and Ryohei Miyadera, Jan 17 2006

Keywords

• easy
• cons
• nonn

Comments

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

Examples

			0.00011122233344455566677788900011...
		

References

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

Links

• Index entries for linear recurrences with constant coefficients, 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).

Crossrefs

Cf. A002264, A021895.

Programs

Mathematica

m = 17; Sqrt[Apply[Plus, 576*Table[(10^3)^k, {k, 0, m}]]]
Join[{0,0,0},RealDigits[1/8991,10,120][[1]]] (* Harvey P. Dale, Apr 22 2012 *)

Formula

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

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