A269993
Denominators of r-Egyptian fraction expansion for sqrt(1/2), where r = (1,1/2,1/3,1/4,...)
Original entry on oeis.org
2, 3, 9, 74, 8098, 101114070, 10080916639334518, 234737156891222571756748160861129, 104728182461244680288139397973895577148266725366426255244889745185
Offset: 1
sqrt(1/2) = 1/2 + 1/(2*3) + 1/(3*9) + ...
-
r[k_] := 1/k; f[x_, 0] = x; z = 10;
n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]
f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]
x = Sqrt[1/2]; Table[n[x, k], {k, 1, z}]
-
r(k) = 1/k;
x = sqrt(1/2);
f(x, k) = if(k<1, x, f(x, k - 1) - r(k)/n(x, k));
n(x, k) = ceil(r(k)/f(x, k - 1));
for(k = 1, 10, print1(n(x, k),", ")) \\ Indranil Ghosh, Mar 27 2017, translated from Mathematica code
A224231
Egyptian fraction expansion of sqrt(3).
Original entry on oeis.org
1, 2, 5, 32, 1249, 5986000, 438522193400489, 3126430743599145840898147625516, 10008815260914521335142941393259537613217919681721512170785592
Offset: 0
sqrt(3) = 1 + 1/2 + 1/5 + 1/32 + 1/1249 + 1/5986000 + ...
A118325 is the main entry for this sequence.
A144835
Denominators of an Egyptian fraction for 1/zeta(2) = 0.607927101854... (A059956).
Original entry on oeis.org
2, 10, 127, 18838, 522338493, 727608914652776081, 990935377560451600699026552443764271, 1223212384013602554473872691328685513734082755736750146553750539914774364
Offset: 1
1/zeta(2) = 0.607927101854... = 1/2 + 1/10 + 1/127 + 1/18838 + ...
- Amiram Eldar, Table of n, a(n) for n = 1..11
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342.
- Eric Weisstein's World of Mathematics, Egyptian Fraction.
- Index entries for sequences related to Egyptian fractions.
Cf.
A001466,
A006487,
A006524,
A006525,
A006526,
A059956,
A069139,
A110820,
A117116,
A118323,
A118324,
A118325.
-
a = {}; k = N[1/Zeta[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
-
x=1/zeta(2); while(x, t=1\x+1; print1(t", "); x -= 1/t) \\ Charles R Greathouse IV, Nov 08 2013
A144984
Denominators of an Egyptian fraction for 1/sqrt(5) (A020762).
Original entry on oeis.org
3, 9, 362, 148807, 432181530536, 615828580117398011389583, 385329014801969222669766835659574445455872858297
Offset: 1
Cf.
A020762,
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003.
-
a = {}; k = N[1/Sqrt[5], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
A145003
Denominators of an Egyptian fraction for 1/sqrt(29) = 0.185695338... (A020786).
Original entry on oeis.org
6, 53, 6221, 891830563, 950677235679298964, 2245647960428048728674383451656707058, 11636905679093503238901947768600244923435901955366623291532461461126244496
Offset: 1
Cf.
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003.
-
a = {}; k = N[1/Sqrt[29], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
A144983
Denominators of greedy Egyptian fraction for 1/sqrt(3) (A020760).
Original entry on oeis.org
2, 13, 2341, 41001128, 3352885935529869, 17147396444547741051849884001699, 1847333322606272250132077006229901193256553492442739965269739579
Offset: 1
Cf.
A001466,
A006487,
A006524,
A006525,
A006526,
A020760,
A069139,
A069261,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A144984-
A145003.
-
a = {}; k = N[1/Sqrt[3], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
A142725
Denominators of an Egyptian fraction for 1/Sqrt[17] = 0.242535625...
Original entry on oeis.org
5, 24, 1151, 6727710, 97954001297811, 12083213443785578998604325741, 2111557350230332542969297514824119073134312726162508784857, 5126406954746155312559668571658555244727150562238830979161154018392336359308299948544053564102183773577991816755308
Offset: 1
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003
-
a = {}; k = N[1/Sqrt[17], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)
A142726
Denominators of an Egyptian fraction for 1/Sqrt[20] = 0.2236067977...
Original entry on oeis.org
5, 43, 2850, 9380555, 131539825706327, 25568462906010064277774504354, 1702783284378767791750994476557209698496292570221862357616, 9282809298390896944529722953873240985108041182275536393531898614770319137100914187360035180181565645720539192811580
Offset: 1
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003
-
a = {}; k = N[1/Sqrt[20], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)
A144985
Denominators of an Egyptian fraction for 1/Sqrt[6]=0.408248290463863...
Original entry on oeis.org
3, 14, 287, 484228, 624850913463, 832896370765715143490072, 7620764031777359266114991754446899201236457828088, 74466937067918173179787895367258766085493130434332689333832927329763999409894621431449951498850730
Offset: 1
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003
-
a = {}; k = N[1/Sqrt[6], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)
A144986
Denominators of an Egyptian fraction for 1/Sqrt[7]=0.377964473...
Original entry on oeis.org
3, 23, 868, 1242123, 2776290405248, 11161696107523243223922840, 261638153821481209775970282548980739821715625184617, 189055393361766552088064316219614698328133697744770641431804048878604165927723712902309210241320415402
Offset: 1
A069139,
A006487,
A006526,
A006525,
A006524,
A001466,
A110820,
A117116,
A118323,
A118324,
A118325,
A144835,
A132480-
A132574,
A069261,
A144984-
A145003
-
a = {}; k = N[1/Sqrt[7], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)
Showing 1-10 of 26 results.
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