A021053 Decimal expansion of 1/49.

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

Offset

0,2

Comments

The 42-digit cycle 1,0,2,0,4,0,8,1,6,3,2,6,5,3,0,6,1,2,2,4,4,8,9,7,9,5,9,1,8,3,6,7,3,4,6,9,3,8,7,7,5,5 in this sequence and the others based on forty-ninths, gives the successive digits of the smallest integer which is multiplied by 5 when the final digit is moved from the right hand end to the left hand end. - Ian Duff, Jan 09 2009

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 78.

Links

Table of n, a(n) for n=0..98.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

Formula

From Chai Wah Wu, Jul 13 2016: (Start)

a(n) = a(n-1) - a(n-21) + a(n-22) for n > 21.

G.f.: x*(x^20 + 4*x^19 + 2*x^17 + x^15 - 5*x^14 + 6*x^13 - 3*x^12 - 2*x^11 - x^10 + 4*x^9 - x^8 - 3*x^7 + 5*x^6 - 7*x^5 + 8*x^4 - 4*x^3 + 4*x^2 - 2*x + 2)/(1 - x + x^21 - x^22). (End)

Example

0.020408163265306122448979591836...

Mathematica

PadLeft[First@ #, Length@ First@ # + Abs@ Last@ #] &@ RealDigits[N[1/49, 120]] (* Michael De Vlieger, Jul 13 2016 *)

Prog

(PARI) 1/49. \\ Altug Alkan, Jul 13 2016

Crossrefs

Sequence in context: A077966 A275670 A021102 * A182443 A128983 A265833

Adjacent sequences: A021050 A021051 A021052 * A021054 A021055 A021056

Keyword

nonn,cons

Author

N. J. A. Sloane.

Status

approved