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A156736 Signed greedy Egyptian fraction for Pi/2 1
1, 2, 14, -1582, -7497258, 303297921775458, -2646995089135122277190614296178, 82888930564911423983289917045230098319343306166666586941750246 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The second and fourth convergents of Pi (22/7 and 355/113) appear when truncating the series to three and four terms.

LINKS

Table of n, a(n) for n=0..7.

Wikipedia, Greedy algorithm for Egyptian fractions

FORMULA

Sum(n>=0,1/a(n))=Pi/2.

a(n) = 2*A001467(n+1). - R. J. Mathar, Apr 02 2011

EXAMPLE

1+1/2+1/14=11/7=(1/2)(22/7)

1+1/2+1/14-1/1582=355/226=(1/2)(355/113)

PROG

(PARI) x=Pi/2; for (k=0, 7, d=round(1/x); x=x-1/d; print1(d, ", "))

CROSSREFS

Cf. A001466, A156269, A156618.

Cf. A156750. [From Jaume Oliver Lafont, Mar 03 2009]

Sequence in context: A130421 A347908 A227403 * A334247 A277288 A296412

Adjacent sequences:  A156733 A156734 A156735 * A156737 A156738 A156739

KEYWORD

sign

AUTHOR

Jaume Oliver Lafont, Feb 14 2009

STATUS

approved

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Last modified October 21 17:37 EDT 2021. Contains 348155 sequences. (Running on oeis4.)