A154925 - OEIS

A154925

The terms of this sequence are integer values of consecutive denominators (with signs) from the fractional expansion (using only fractions with numerators to be positive 1's) of the BBP polynomial ( 4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6) ) for all k (starting from 0 to infinity).

1, 1, 1, 1, -2, -5, -6, 3, 9, -5, -13, -14, 5, 30, 510, -10, -21, -22, 7, 59, 5163, 53307975, -14, -29, -30

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OFFSET

0,5

COMMENTS

The Egyptian fraction expansion is applied to the first fraction (that is, 4/(8*k+1) ) of the BBP polynomial ( 4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6) ) for k >= 1. R. Knott's converter calculator #1 (http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html#calc1) is used for such conversion. Note that in the case of k=0, 4/(8*k+1) = 4 and could be trivially expressed as 1/1 + 1/1 + 1/1 + 1/1. It remains to be seen how the above described Pi presentation relates to Engel's presentation of Pi, which also consists of an infinite sum of fractions whose numerators are all 1's.

LINKS

Table of n, a(n) for n=0..24.

Wikipedia, Bailey-Borwein-Plouffe formula.

EXAMPLE

For k=1, 4/(8*k+1) = 4/9 = 1/3 + 1/9, thus the first (smallest) denominator is 3 so a(7)=3.

For k=1, 4/(8*k+1) = 4/9 = 1/3 + 1/9 and the second (next to smallest) denominator is 9 so a(8)=9.

CROSSREFS

Cf. A154429.

Sequence in context: A340858 A309364 A062825 * A154962 A091655 A362977

Adjacent sequences: A154922 A154923 A154924 * A154926 A154927 A154928

KEYWORD

sign,uned

AUTHOR

Alexander R. Povolotsky, Jan 17 2009, Jan 18 2009

STATUS

approved