Displaying 1-10 of 111 results found.
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Egyptian fraction representation of sqrt(5) ( A002163) using a greedy function.
+10
89
2, 5, 28, 2828, 11765225, 244616741135815, 200345939091917238204751820525, 58201747163932603551486315260692070868016224421408235882974, 3950825087286888657146721201016118914863842749907092675300186489072730656660851348699680127901879302396406080621599015
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 5]]
Egyptian fraction representation of sqrt(99) ( A010550) using a greedy function.
+10
88
9, 2, 3, 9, 185, 40782, 1682066752, 6363269744807224762, 71990770113177468702243288679736023556, 7052581923050601721615256905785412578772858487621807510338728141989919040612
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 99]]
Denominators of an Egyptian fraction for 1/sqrt(5) ( A020762).
+10
23
3, 9, 362, 148807, 432181530536, 615828580117398011389583, 385329014801969222669766835659574445455872858297
MATHEMATICA
a = {}; k = N[1/Sqrt[5], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
CROSSREFS
Cf. A020762, A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480- A132574, A069261, A144984- A145003.
Denominators of an Egyptian fraction for 1/sqrt(29) = 0.185695338... ( A020786).
+10
23
6, 53, 6221, 891830563, 950677235679298964, 2245647960428048728674383451656707058, 11636905679093503238901947768600244923435901955366623291532461461126244496
MATHEMATICA
a = {}; k = N[1/Sqrt[29], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
CROSSREFS
Cf. A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480- A132574, A069261, A144984- A145003.
Denominators of greedy Egyptian fraction for 1/sqrt(3) ( A020760).
+10
2
2, 13, 2341, 41001128, 3352885935529869, 17147396444547741051849884001699, 1847333322606272250132077006229901193256553492442739965269739579
MATHEMATICA
a = {}; k = N[1/Sqrt[3], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
CROSSREFS
Cf. A001466, A006487, A006524, A006525, A006526, A020760, A069139, A069261, A110820, A117116, A118323, A118324, A118325, A144835, A132480- A132574, A144984- A145003.
Egyptian fraction representation of sqrt(22) ( A010478) using a greedy function.
+10
2
4, 2, 6, 43, 2028, 5477762, 40063230724280, 10039617492048087897098971783, 598943577818423089223821862011302605314284839297545338532, 451273778419286656581820003198742640276389207705020449590295850757882195737121214614786626350432663721793231915121
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 22]]
Egyptian fraction representation of sqrt(10) ( A010467) using a greedy function.
+10
1
3, 7, 52, 5271, 32510519, 1551821465402536, 2553352811042166137014681056617, 6785214292790116540717856342564735260380655042140053309985580, 57499324177051573068556985649019772314982410954417460069917198506894068347777607349711324456505504280305966462257432295349
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 10]]
Egyptian fraction representation of sqrt(13) ( A010470) using a greedy function.
+10
1
3, 2, 10, 181, 37860, 2063394882, 20133724366323386460, 895769948382354175062611801976979893814, 1095684829796116398764171865109547325653507924058299202087102696023776712107256
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter >
0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 13]]
Egyptian fraction representation of sqrt(17) ( A010473) using a greedy function.
+10
1
4, 9, 84, 11142, 474347339, 1448582974451426406, 2526762018809024624337804813995389534, 28249016389028465904997590221278194109894254535234000317524709009386354668
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter >
0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 17]]
Egyptian fraction representation of sqrt(21) ( A010477) using a greedy function.
+10
1
4, 2, 13, 177, 344766, 1649432522483, 3009384963228815398356405, 9085726642856091334926418336934724393317743509110, 200625769243543756748406312378876010708020812606355642597458369416042779347013395136132184521789202
MATHEMATICA
Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 21]]
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