1,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.

J. W. Wrench, Jr., personal communication.

S. Plouffe, Table of n, a(n) for n = 1..11 [There is a limit of about 1000 digits on the size of numbers in b-files]

Index entries for sequences related to the number Pi

S. Plouffe, Table of n, a(n) for n = 1..14

Eric Weisstein's World of Mathematics, Egyptian Fraction

lst={}; k=N[(Pi-3), 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]

Sequence in context: A071401 A081907 A080525 this_sequence A082179 A044527 A056054

Adjacent sequences: A001463 A001464 A001465 this_sequence A001467 A001468 A001469

nonn

N. J. A. Sloane (njas(AT)research.att.com).

0,2

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Index entries for sequences related to Egyptian fractions

Eric Weisstein's World of Mathematics, Egyptian Fraction

lst={}; k=N[Sqrt[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]

Sequence in context: A036680 A111431 A015701 this_sequence A042823 A132560 A128385

Adjacent sequences: A006484 A006485 A006486 this_sequence A006488 A006489 A006490

nonn

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

0,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

lst={}; k=N[E-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]

Sequence in context: A114029 A013171 A073422 this_sequence A042161 A101151 A138788

Adjacent sequences: A006522 A006523 A006524 this_sequence A006526 A006527 A006528

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from H. P. Robinson.

0,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Index entries for sequences related to the number Pi

Index entries for sequences related to Egyptian fractions

Eric Weisstein's World of Mathematics, Egyptian Fraction

a = {}; k = N[1/Pi, 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]

Sequence in context: A048731 A000881 A109923 this_sequence A070037 A153064 A061849

Adjacent sequences: A006521 A006522 A006523 this_sequence A006525 A006526 A006527

nonn

N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

More terms from H. P. Robinson.

0,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

a = {}; k = N[1/E, 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]

Sequence in context: A162085 A003190 A133663 this_sequence A139517 A156026 A112981

Adjacent sequences: A006523 A006524 A006525 this_sequence A006527 A006528 A006529

nonn

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

0,1

Index entries for sequences related to Egyptian fractions

Eric Weisstein's World of Mathematics, Egyptian Fraction

a(n) =ceiling[1/sqrt(2)-Sum_i{i<n}1/a(i)]

a(3)=68575 since sqrt(1/2)=0.707106781186..., 1/2+1/5+1/141+1/68574=0.707106781368... (which is too much) and 1/2+1/5+1/141+1/68575=0.707106781155... (which is not too much).

a = {}; k = N[1/Sqrt[2], 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]

Cf. A006487.

Sequence in context: A088271 A145620 A130412 this_sequence A155762 A062611 A041505

Adjacent sequences: A069136 A069137 A069138 this_sequence A069140 A069141 A069142

nonn

Henry Bottomley (se16(AT)btinternet.com), Apr 08 2002

1,1

Eric Weisstein's World of Mathematics, Egyptian Fraction

a(3)=ceil[1/(0.5772156649...-1/2-1/13)]=3418.

a = {}; k = N[EulerGamma, 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]

Sequence in context: A158026 A103641 A144983 this_sequence A139519 A111016 A118912

Adjacent sequences: A110817 A110818 A110819 this_sequence A110821 A110822 A110823

nonn,frac

Franz Vrabec (franz.vrabec(AT)aon.at), Sep 16 2005

0,2

For each term, the largest possible unit fraction is used.

Eric Weisstein's World of Mathematics, Egyptian Fraction

D. Eppstein, Algorithms for Egyptian Fractions

a(4)=145 because 1/145 is the largest unit fraction less than phi-1/1-1/2-1/9.

a = {1}; k = N[(Sqrt[5] - 1)/2, 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]

Cf. A001622.

Sequence in context: A110817 A110860 A050995 this_sequence A133468 A081459 A038843

Adjacent sequences: A117113 A117114 A117115 this_sequence A117117 A117118 A117119

nonn

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Apr 19 2006

Edited by Don Reble (djr(AT)nk.ca), Apr 21 2006

0,1

The next term in the series, a(7), is ~10^95.

Sequence in context: A028337 A135014 A092024 this_sequence A053608 A123261 A124061

Adjacent sequences: A069258 A069259 A069260 this_sequence A069262 A069263 A069264

easy,frac,nonn

Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

1,1

1/zeta_2 = 1/1.644934067... = 0.607927101854...=1/2+1/10+1/127+1/18838+...+a[n] n->Infinity

a = {}; k = N[1/Zeta[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)

A001466, A006487, A006524, A006525, A006526, A069139, A110820, A117116, A118323, A118324, A118325,

Sequence in context: A013038 A005321 A092645 this_sequence A119191 A125993 A011805

Adjacent sequences: A144832 A144833 A144834 this_sequence A144836 A144837 A144838

frac,nonn

Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008