A215712 Numerator of sum(i=1..n, 3*i/4^i )

3, 9, 81, 21, 1359, 2727, 21837, 21843, 349515, 699045, 5592393, 2796201, 89478471, 178956963, 1431655749, 1431655761, 22906492227, 45812984481, 366503875905, 22906492245, 5864062014783, 11728124029599, 93824992236861, 93824992236879, 1501199875790139

Offset

1,1

Comments

The limit as n goes to infinity is 4/3.

References

Calvin C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 96.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

a(4) = 21 because 3/4 + 6/16 + 9/64 + 12/256 = 3/4 + 3/8 + 9/64 + 3/64 = 48/64 + 24/64 + 9/64 + 3/64 = 84/64 = 21/16.

Mathematica

Table[Numerator[Sum[3i/4^i, {i, n}]], {n, 40}]

Prog

(Magma) [Numerator(&+[3*i/4^i: i in [1..n]]): n in [1..25]]; // Bruno Berselli, Sep 03 2012

Crossrefs

Cf. A215713 for the denominators.

A036295/A036296 is the same with i/2^i instead of 3i/4^i.

Cf. A122553.

Sequence in context: A032330 A018604 A301535 * A000218 A139731 A259986

Adjacent sequences: A215709 A215710 A215711 * A215713 A215714 A215715

Keyword

nonn,easy,frac

Author

Alonso del Arte, Aug 21 2012

Extensions

a(17) corrected by Vincenzo Librandi, Sep 04 2012

Status

approved