A215713 Denominator of sum(i=1..n, 3*i/4^i).

4, 8, 64, 16, 1024, 2048, 16384, 16384, 262144, 524288, 4194304, 2097152, 67108864, 134217728, 1073741824, 1073741824, 17179869184, 34359738368, 274877906944, 17179869184, 4398046511104, 8796093022208, 70368744177664, 70368744177664, 1125899906842624

Offset: 1

Author

Alonso del Arte, Aug 21 2012

Keywords

• nonn
• easy
• frac

Comments

The odd-indexed terms are the even-indexed powers of 4 (A013709).

Examples

			a(4) = 16 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.
		

References

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

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A215712 for the numerators. A036295/A036296 is very similar but with i/2^i instead of 3i/4^i. Cf. also A122553.

Programs

Magma

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

Mathematica

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

PARI

vector(100, n, denominator(sum(i=1, n, 3*i/4^i))) \\ Colin Barker, Nov 09 2014