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Search: "greedy egyptian fraction expansion"
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| A118323 |
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(Greedy) Egyptian fraction expansion of Catalan constant. |
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+20
31
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| 2, 3, 13, 176, 36543, 1394774578, 12493702893882521837, 265316559833226727589598741150947701321
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Egyptian Fraction
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EXAMPLE
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Catalan constant = 1/2 + 1/3 + 1/13 + 1/176 + 1/36543 + ...
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MATHEMATICA
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a = {}; k = N[Catalan, 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]
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CROSSREFS
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Cf. A006752.
Cf. A006752, A104338, A014538, A153069, A153070, A054543. - Stuart Clary (clary(AT)uakron.edu), Dec 17, 2008
Sequence in context: A137459 A072162 A113785 this_sequence A113494 A139520 A132535
Adjacent sequences: A118320 A118321 A118322 this_sequence A118324 A118325 A118326
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Apr 23, 2006
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| A118324 |
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(Greedy) Egyptian fraction expansion of ln(2). |
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+20
26
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| 2, 6, 38, 6071, 144715221, 58600453312405245, 28261174043083404192255923187258021, 1350299665604204277005894785275782053022737307184211775676631561245153
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Egyptian Fraction
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EXAMPLE
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ln(2) = 1/2 + 1/6 + 1/38 + 1/6071 + 1/144715221 + ...
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MATHEMATICA
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lst={}; k=N[Log[2], 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 02 2009]
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PROGRAM
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(PARI) x=log(2); for (k=1, 8, d=ceil(1/x); x=x-1/d; print(d)) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 24 2009]
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CROSSREFS
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Cf. A002162.
Sequence in context: A057297 A005530 A072191 this_sequence A060421 A054970 A120492
Adjacent sequences: A118321 A118322 A118323 this_sequence A118325 A118326 A118327
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Apr 23, 2006
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EXTENSIONS
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a(8) from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 24 2009
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| A118325 |
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(Greedy) Egyptian fraction expansion of frac(sqrt(3)) = sqrt(3)-1. |
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+20
25
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| 2, 5, 32, 1249, 5986000, 438522193400489, 3126430743599145840898147625516, 10008815260914521335142941393259537613217919681721512170785592
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Egyptian Fraction
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EXAMPLE
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sqrt(3)-1 = 1/2 + 1/5 + 1/32 + 1/1249 + 1/5986000 + ...
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MATHEMATICA
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lst={}; k=N[(Sqrt[3]-1), 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 02 2009]
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CROSSREFS
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Cf. A002194.
Sequence in context: A019036 A005636 A067299 this_sequence A019037 A019038 A114793
Adjacent sequences: A118322 A118323 A118324 this_sequence A118326 A118327 A118328
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Apr 23, 2006
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| A123180 |
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Even positions of Sylvester's sequence A000058; the denominators of the (greedy) Egyptian fraction expansion of Cahen's constant. |
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+20
1
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| A157193 |
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Greedy Egyptian fraction expansion for 4/Pi |
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+20
1
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| 1, 4, 44, 1953, 4179942, 42836179578838, 3958573977160882295479936105, 36328295343356352083453782833218820307659379901717630389
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum_{n>=0}1/a(n)=4/Pi
Truncating the series to three terms yields the convergent 22/7 as an approximation to Pi:
1+1/4+1/44=14/11=4/(22/7)
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LINKS
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Wikipedia, Greedy algorithm for Egyptian fractions
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PROGRAM
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(PARI) x=4/Pi; for (k=0, 7, d=ceil(1/x); x=x-1/d; print(d, ", "))
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CROSSREFS
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Cf. A088538, A154956, A156618.
Sequence in context: A155556 A127635 A134174 this_sequence A024254 A167781 A075029
Adjacent sequences: A157190 A157191 A157192 this_sequence A157194 A157195 A157196
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KEYWORD
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frac,nonn
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 24 2009
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| A157718 |
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Greedy Egyptian fraction expansion of log(3). |
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+20
1
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| 1, 11, 130, 91827, 42593758221, 2068726045016880942060, 20697114911379630588051784011292634933847536, 83276947012925347630278047002339585844748738907354795550015802020488552337404880\ 3963217
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Wikipedia, Greedy algorithm for Egyptian fractions
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EXAMPLE
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log(3) = Sum_{n>=0} 1/a(n) = 1/1 + 1/11 + 1/130 + 1/91827 + 1/42593758221 + ...
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PROGRAM
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(PARI) x=log(3); for (k=1, 8, d=ceil(1/x); x=x-1/d; print(d, ", "))
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CROSSREFS
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Cf. A058962, A154920, A157024, A002391, A118324.
Sequence in context: A024144 A015602 A015603 this_sequence A046210 A100757 A099677
Adjacent sequences: A157715 A157716 A157717 this_sequence A157719 A157720 A157721
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KEYWORD
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frac,nonn
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 04 2009
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