A001466 -id:A001466 - cp's OEIS frontend

A000918 a(n) = 2^n - 2.

-1, 0, 2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590, 17179869182, 34359738366, 68719476734, 137438953470

Offset: 0

N. J. A. Sloane

For n > 1, a(n) is the expected number of tosses of a fair coin to get n-1 consecutive heads. - Pratik Poddar, Feb 04 2011
For n > 2, Sum_{k=1..a(n)} (-1)^binomial(n, k) = A064405(a(n)) + 1 = 0. - Benoit Cloitre, Oct 18 2002
For n > 0, the number of nonempty proper subsets of an n-element set. - Ross La Haye, Feb 07 2004
Numbers j such that abs( Sum_{k=0..j} (-1)^binomial(j, k)*binomial(j + k, j - k) ) = 1. - Benoit Cloitre, Jul 03 2004
For n > 2 this formula also counts edge-rooted forests in a cycle of length n. - Woong Kook (andrewk(AT)math.uri.edu), Sep 08 2004
For n >= 1, conjectured to be the number of integers from 0 to (10^n)-1 that lack 0, 1, 2, 3, 4, 5, 6 and 7 as a digit. - Alexandre Wajnberg, Apr 25 2005
Beginning with a(2) = 2, these are the partial sums of the subsequence of A000079 = 2^n beginning with A000079(1) = 2. Hence for n >= 2 a(n) is the smallest possible sum of exactly one prime, one semiprime, one triprime, ... and one product of exactly n-1 primes. A060389 (partial sums of the primorials, A002110, beginning with A002110(1)=2) is the analog when all the almost primes must also be squarefree. - Rick L. Shepherd, May 20 2005
From the second term on (n >= 1), the binary representation of these numbers is a 0 preceded by (n - 1) 1's. This pattern (0)111...1110 is the "opposite" of the binary 2^n+1: 1000...0001 (cf. A000051). - Alexandre Wajnberg, May 31 2005
The numbers 2^n - 2 (n >= 2) give the positions of 0's in A110146. Also numbers k such that k^(k + 1) = 0 mod (k + 2). - Zak Seidov, Feb 20 2006
Partial sums of A155559. - Zerinvary Lajos, Oct 03 2007
Number of surjections from an n-element set onto a two-element set, with n >= 2. - Mohamed Bouhamida, Dec 15 2007
It appears that these are the numbers n such that 3*A135013(n) = n*(n + 1), thus answering Problem 2 on the Mathematical Olympiad Foundation of Japan, Final Round Problems, Feb 11 1993 (see link Japanese Mathematical Olympiad).
Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x is a proper subset of y or y is a proper subset of x and x and y are disjoint. Then a(n+1) = |R|. - Ross La Haye, Mar 19 2009
The permutohedron Pi_n has 2^n - 2 facets [Pashkovich]. - Jonathan Vos Post, Dec 17 2009
First differences of A005803. - Reinhard Zumkeller, Oct 12 2011
For n >= 1, a(n + 1) is the smallest even number with bit sum n. Cf. A069532. - Jason Kimberley, Nov 01 2011
a(n) is the number of branches of a complete binary tree of n levels. - Denis Lorrain, Dec 16 2011
For n>=1, a(n) is the number of length-n words on alphabet {1,2,3} such that the gap(w)=1. For a word w the gap g(w) is the number of parts missing between the minimal and maximal elements of w. Generally for words on alphabet {1,2,...,m} with g(w)=g>0 the e.g.f. is Sum_{k=g+2..m} (m - k + 1)*binomial((k - 2),g)*(exp(x) - 1)^(k - g). a(3)=6 because we have: 113, 131, 133, 311, 313, 331. Cf. A240506. See the Heubach/Mansour reference. - Geoffrey Critzer, Apr 13 2014
For n > 0, a(n) is the minimal number of internal nodes of a red-black tree of height 2*n-2. See the Oct 02 2015 comment under A027383. - Herbert Eberle, Oct 02 2015
Conjecture: For n>0, a(n) is the least m such that A007814(A000108(m)) = n-1. - L. Edson Jeffery, Nov 27 2015
Actually this follows from the procedure for determining the multiplicity of prime p in C(n) given in A000108 by Franklin T. Adams-Watters: For p=2, the multiplicity is the number of 1 digits minus 1 in the binary representation of n+1. Obviously, the smallest k achieving "number of 1 digits" = k is 2^k-1. Therefore C(2^k-2) is divisible by 2^(k-1) for k > 0 and there is no smaller m for which 2^(k-1) divides C(m) proving the conjecture. - Peter Schorn, Feb 16 2020
For n >= 0, a(n) is the largest number you can write in bijective base-2 (a.k.a. the dyadic system, A007931) with n digits. - Harald Korneliussen, May 18 2019
The terms of this sequence are also the sum of the terms in each row of Pascal's triangle other than the ones. - Harvey P. Dale, Apr 19 2020
For n > 1, binomial(a(n),k) is odd if and only if k is even. - Charlie Marion, Dec 22 2020
For n >= 2, a(n+1) is the number of n X n arrays of 0's and 1's with every 2 X 2 square having density exactly 2. - David desJardins, Oct 27 2022
For n >= 1, a(n+1) is the number of roots of unity in the unique degree-n unramified extension of the 2-adic field Q_2. Note that for each p, the unique degree-n unramified extension of Q_p is the splitting field of x^(p^n) - x, hence containing p^n - 1 roots of unity for p > 2 and 2*(2^n - 1) for p = 2. - Jianing Song, Nov 08 2022

			a(4) = 14 because the 14 = 6 + 4 + 4 rationals (in lowest terms) for n = 3 are (see the Jun 14 2017 formula above): 1/2, 1, 3/2, 2, 5/2, 3; 1/4, 3/4, 5/4, 7/4; 1/8, 3/8, 5/8, 7/8. - _Wolfdieter Lang_, Jun 14 2017

H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 212.
Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition, Addison-Wesley, 2004, p. 134. - Mohammad K. Azarian, Oct 27 2011
S. Heubach and T. Mansour, Combinatorics of Compositions and Words, Chapman and Hall, 2009 page 86, Exercise 3.16.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 33.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911, p. 31.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Andrei Asinowski, Cyril Banderier, and Benjamin Hackl, Flip-sort and combinatorial aspects of pop-stack sorting, arXiv:2003.04912 [math.CO], 2020.
O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
S. Bilotta, E. Grazzini, and E. Pergola, Enumeration of Two Particular Sets of Minimal Permutations, J. Int. Seq. 18 (2015) 15.10.2
R. B. Campbell, The effect of inbreeding constraints and offspring distribution on time to the most recent common ancestor, Journal of Theoretical Biology, Volume 382, 7 October 2015, Pages 74-80.
Adam M. Goyt and Lara K. Pudwell, Avoiding colored partitions of two elements in the pattern sense, arXiv preprint arXiv:1203.3786 [math.CO], 2012. - From _N. J. A. Sloane_, Sep 17 2012
M. A. Hill, M. J. Hopkins and D. C. Ravenel, On the non-existence of elements of Kervaire invariant one. - _N. J. A. Sloane_, Sep 27 2010
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 77
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Milan Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Japanese Mathematical Olympiad 1993, Final Round - Problem 2, Feb 11 1993.
Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
T. Manneville, V. Pilaud, Compatibility fans for graphical nested complexes, arXiv preprint arXiv:1501.07152 [math.CO], 2015.
Kanstantsin Pashkovich, Symmetry in Extended Formulations of the Permutahedron [sic], arXiv:0912.3446 [math.CO], 2009-2013. [_Jonathan Vos Post_, Dec 17 2009]
P. A. Piza, Kummer numbers, Mathematics Magazine, 21 (1947/1948), 257-260.
P. A. Piza, Kummer numbers, Mathematics Magazine, 21 (1947/1948), 257-260. [Annotated scanned copy]
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Pratik Poddar, Consecutive Heads Puzzle, Oct 2009.
H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911. [Annotated scans of pages 30-33 only]
Eric Weisstein's World of Mathematics, Sphere Line Picking
Index entries for linear recurrences with constant coefficients, signature (3,-2).
Index to sequences related to Olympiads.

Row sums of triangle A026998.
Cf. A000919, A001117, A001118, A095121, A110146.
Cf. A033484, A000225, A000325, A095151, A125128.
Cf. A058809 (3^n-3, n>0).

a000918 = (subtract 2) . (2 ^)
a000918_list = iterate ((subtract 2) . (* 2) . (+ 2)) (- 1)
-- Reinhard Zumkeller, Apr 23 2013

[2^n - 2: n in [0..40]]; // Vincenzo Librandi, Jun 23 2011

Maple
```
seq(2^n-2,n=0..20) ;
```

Table[2^n - 2, {n, 0, 29}] (* Alonso del Arte, Dec 01 2012 *)

a(n)=2^n-2 \\ Charles R Greathouse IV, Jun 16 2011

def A000918(n): return (1<Chai Wah Wu, Jun 10 2025

a(n) = 2*A000225(n-1).
G.f.: 1/(1 - 2*x) - 2/(1 - x), e.g.f.: (e^x - 1)^2 - 1. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001
For n >= 1, a(n) = A008970(n + 1, 2). - Philippe Deléham, Feb 21 2004
G.f.: (3*x - 1)/((2*x - 1)*(x - 1)). - Simon Plouffe in his 1992 dissertation for the sequence without the leading -1
a(n) = 2*a(n - 1) + 2. - Alexandre Wajnberg, Apr 25 2005
a(n) = A000079(n) - 2. - Omar E. Pol, Dec 16 2008
a(n) = A058896(n)/A052548(n). - Reinhard Zumkeller, Feb 14 2009
a(n) = A164874(n - 1, n - 1) for n > 1. - Reinhard Zumkeller, Aug 29 2009
a(n) = A173787(n,1); a(n) = A028399(2*n)/A052548(n), n > 0. - Reinhard Zumkeller, Feb 28 2010
a(n + 1) = A027383(2*n - 1). - Jason Kimberley, Nov 02 2011
G.f.: U(0) - 1, where U(k) = 1 + x/(2^k + 2^k/(x - 1 - x^2*2^(k + 1)/(x*2^(k + 1) - (k + 1)/U(k + 1) ))); (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Dec 01 2012
a(n+1) is the sum of row n in triangle A051601. - Reinhard Zumkeller, Aug 05 2013
a(n+1) = A127330(n,0). - Reinhard Zumkeller, Nov 16 2013
a(n) = Sum_{k=1..n-1} binomial(n, k) for n > 0. - Dan McCandless, Nov 14 2015
From Miquel Cerda, Aug 16 2016: (Start)
a(n) = A000225(n) - 1.
a(n) = A125128(n-1) - A000325(n).
a(n) = A095151(n) - A125128(n) - 1. (End)
a(n+1) = 2*(n + Sum_{j=1..n-1} (n-j)*2^(j-1)), n >= 1. This is the number of the rationals k/2, k = 1..2*n for n >= 1 and (2*k+1)/2^j for j = 2..n, n >= 2, and 2*k+1 < n-(j-1). See the example for n = 3 below. Motivated by the proposal A287012 by Mark Rickert. - Wolfdieter Lang, Jun 14 2017

Maple programs fixed by Vaclav Kotesovec, Dec 13 2014

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

Clark Kimberling, Mar 15 2016

Suppose that r is a sequence of rational numbers r(k) <= 1 for k >= 1, and that x is an irrational number in (0,1).  Let f(0) = x, n(k) = floor(r(k)/f(k-1)), and f(k) = f(k-1) - r(k)/n(k).  Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ... , the r-Egyptian fraction for x.
Guide to related sequences:
r(k)               x               denominators
1               sqrt(1/2)             A069139
1               sqrt(1/3)             A144983
1               sqrt(2) - 1           A006487
1               sqrt(3) - 1           A118325
1               tau - 1               A117116
1               1/Pi                  A006524
1               Pi-3                  A001466
1               1/e                   A006526
1                e - 2                A006525
1               log(2)                A118324
1               Euler constant        A110820
1               (1/2)^(1/3)           A269573
.
1/k             sqrt(1/2)             A269993
1/k             sqrt(1/3)             A269994
1/k             sqrt(2) - 1           A269995
1/k             sqrt(3) - 1           A269996
1/k             tau - 1               A269997
1/k             1/Pi                  A269998
1/k             Pi-3                  A269999
1/k             1/e                   A270001
1/k             e - 2                 A270002
1/k             log(2)                A270314
1/k             Euler constant        A270315
1/k             (1/2)^(1/3)           A270316
.
Using the 12 choices for x shown above (that is, sqrt(1/2) to (1/2)^(1/3)), the denominator sequence of the r-Egyptian fraction for x appears for each of the following sequences (r(k)):
r(k) = 1 (see above)
r(k) = 1/k (see above)
r(k) = 2^(1-k):  A270347-A270358
r(k) = 1/Fibonacci(k+1):  A270394-A270405
r(k) = 1/prime(k):  A270476-A270487
r(k) = 1/k!:  A270517-A270527 (A000027 for x = e - 2)
r(k) = 1/(2k-1):  A270546-A270557
r(k) = 1/(k+1):  A270580-A270591

			sqrt(1/2) = 1/2 + 1/(2*3) + 1/(3*9) + ...

Clark Kimberling, Table of n, a(n) for n = 1..12
Eric Weisstein's World of Mathematics, Egyptian Fraction
Index entries for sequences related to Egyptian fractions

Cf. A269573, A069139, A270347, A270394, A270476, A270517, A270546, A270580.

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

A006525 Denominators of greedy Egyptian fraction for e - 2.

Original entry on oeis.org

2, 5, 55, 9999, 3620211523, 25838201785967533906, 3408847366605453091140558218322023440765

Offset: 1

N. J. A. Sloane

A greedy Egyptian fraction is also called a Sylvester expansion. - Robert FERREOL, May 02 2020

			e - 2 = 1/2 + 1/5 + 1/55 + 1/9999 + ... . - _Jon E. Schoenfield_, Dec 26 2014

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

Vincenzo Librandi, Table of n, a(n) for n = 1..11 [a(11) corrected by _Georg Fischer_, Jun 22 2020]
H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
Eric Weisstein's World of Mathematics, Egyptian Fraction
Wikipedia, Greedy algorithm for Egyptian fractions
Index entries for sequences related to Egyptian fractions

Cf. A006526, A269993.

Cf. A001466 (similar for Pi-3).

lst={};k=N[E-2,1000000];Do[s=Ceiling[1/k];AppendTo[lst,s];k=k-1/s,{n,12}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *)

x = exp(1) - 2;
f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
n(x, k) = ceil(1/f(x, k - 1));
for(k = 1, 7, print1(n(x, k), ", ")) \\ Indranil Ghosh, Mar 27 2017

a(n) = ceiling(1/(e - 2 - Sum_{j=0..n-1} 1/a(j))). - Jon E. Schoenfield, Dec 26 2014

More terms from Herman P. Robinson

Offset changed to 1 by Indranil Ghosh, Mar 27 2017

A006526 Egyptian fraction for 1/e.

Original entry on oeis.org

3, 29, 15786, 513429610, 339840390654894740, 383515880462620946584018566350380249, 226890280396768133952782550246970728734549546771915172071782710229538300

Offset: 0

N. J. A. Sloane, Simon Plouffe

nonn

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

Jinyuan Wang, Table of n, a(n) for n = 0..9
H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
Eric Weisstein's World of Mathematics, Egyptian Fraction.
Index entries for sequences related to Egyptian fractions

Cf. A068985 (1/e).

a = {}; k = N[1/E, 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)

A006524 Egyptian fraction for 1/ Pi.

Original entry on oeis.org

4, 15, 609, 845029, 1010073215739, 1300459886313272270974271, 1939680952094609786557359582286462958434022504402

Offset: 1

N. J. A. Sloane, Robert G. Wilson v

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

Vincenzo Librandi, Table of n, a(n) for n = 1..11 [a(11) corrected by _Georg Fischer_, Jun 04 2019]
H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
Eric Weisstein's World of Mathematics, Egyptian Fraction
Index entries for sequences related to the number Pi
Index entries for sequences related to Egyptian fractions

a = {}; k = N[1/Pi, 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)

x = 1/Pi;
f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
n(x, k) = ceil(1/f(x, k - 1));
for(k = 1, 7, print1(n(x, k),", ")) \\ Indranil Ghosh, Mar 27 2017

More terms from Herman P. Robinson

Offset changed to 1 by Indranil Ghosh, Mar 27 2017

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

Artur Jasinski, Sep 22 2008

			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

Artur Jasinski, Sep 28 2008

Jinyuan Wang, Table of n, a(n) for n = 1..11

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

Artur Jasinski, Sep 28 2008

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

A156618 Denominators of Egyptian fraction for Pi-3 whose partial sums are the convergents.

Original entry on oeis.org

7, -742, 11978, -3740526, 1099482930, -2202719155, 6600663644, -26413901692, 96840976853, -496325469560, 2346251883960, -44006595799206, 1345586183756654, -4127747481719463, 10251870941174304

Offset: 0

Jaume Oliver Lafont, Feb 11 2009

sign

Numerators are all 1.

			3+1/a(0)=22/7
3+1/a(0)+1/a(1)=333/106
3+1/a(0)+1/a(1)+1/a(2)=355/113

Cf. A001466, A014013, A156019, A156020, A002485, A002486.

c0=3; for (k=2,30,m=contfracpnqn(contfrac(Pi,k));c1=m[1,1]/m[2,1];print1(1/(c1-c0),", ");c0=c1;)

A182257 Denominators of Egyptian fraction expansion of Pi.

Original entry on oeis.org

1, 1, 1, 8, 61, 5020, 128541455, 162924332716605980, 28783052231699298507846309644849796, 871295615653899563300996782209332544845605756266650946342214549769447

Offset: 0

N. J. A. Sloane, Apr 21 2012

nonn

Included for completeness. A001466 is the main entry.

Cf. A001466, A224230.

lst={}; k=N[(Pi), 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst (* based on the Mma program from Vladimir Joseph Stephan Orlovsky in A001466 *)

localprec(200); my(v=Pi, d); vector(10, i, v-=1/(d=ceil(1/v)); d) \\ Ruud H.G. van Tol, May 29 2025 (use prec.1200 for 13 terms)

cp's OEIS Frontend

A000918 a(n) = 2^n - 2.

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A269993 Denominators of r-Egyptian fraction expansion for sqrt(1/2), where r = (1,1/2,1/3,1/4,...)

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A006525 Denominators of greedy Egyptian fraction for e - 2.

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A006526 Egyptian fraction for 1/e.

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A006524 Egyptian fraction for 1/ Pi.

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PARI

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A144835 Denominators of an Egyptian fraction for 1/zeta(2) = 0.607927101854... (A059956).

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A144984 Denominators of an Egyptian fraction for 1/sqrt(5) (A020762).

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