A010532 -id:A010532 - cp's OEIS frontend

A248304 Egyptian fraction representation of sqrt(80) (A010532) using a greedy function.

8, 2, 3, 10, 92, 14491, 322744746, 254675920984809222, 106241547612751834703565555273467625, 63822696103699851476352795738044494170110650314781277998043037878782067

Offset: 0

Robert G. Wilson v, Oct 04 2014

nonn

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.

Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

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[ 80]]

A024036 a(n) = 4^n - 1.

Original entry on oeis.org

0, 3, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663, 281474976710655

Offset: 0

N. J. A. Sloane

This sequence is the normalized length per iteration of the space-filling Peano-Hilbert curve. The curve remains in a square, but its length increases without bound. The length of the curve, after n iterations in a unit square, is a(n)*2^(-n) where a(n) = 4*a(n-1)+3. This is the sequence of a(n) values. a(n)*(2^(-n)*2^(-n)) tends to 1, the area of the square where the curve is generated, as n increases. The ratio between the number of segments of the curve at the n-th iteration (A015521) and a(n) tends to 4/5 as n increases. - Giorgio Balzarotti, Mar 16 2006
Numbers whose base-4 representation is 333....3. - Zerinvary Lajos, Feb 03 2007
From Eric Desbiaux, Jun 28 2009: (Start)
It appears that for a given area, a square n^2 can be divided into n^2+1 other squares.
It's a rotation and zoom out of a Cartesian plan, which creates squares with side
= sqrt( (n^2) / (n^2+1) ) --> A010503|A010532|A010541... --> limit 1,
and diagonal sqrt(2*sqrt((n^2)/(n^2+1))) --> A010767|... --> limit A002193.
(End)
Also the total number of line segments after the n-th stage in the H tree, if 4^(n-1) H's are added at the n-th stage to the structure in which every "H" is formed by 3 line segments. A164346 (the first differences of this sequence) gives the number of line segments added at the n-th stage. - Omar E. Pol, Feb 16 2013
a(n) is the cumulative number of segment deletions in a Koch snowflake after (n+1) iterations. - Ivan N. Ianakiev, Nov 22 2013
Inverse binomial transform of A005057. - Wesley Ivan Hurt, Apr 04 2014
For n > 0, a(n) is one-third the partial sums of A002063(n-1). - J. M. Bergot, May 23 2014
Also the cyclomatic number of the n-Sierpinski tetrahedron graph. - Eric W. Weisstein, Sep 18 2017

			G.f. = 3*x + 15*x^2 + 63*x^3 + 255*x^4 + 1023*x^5 + 4095*x^6 + ...

Graham Everest, Alf van der Poorten, Igor Shparlinski, and Thomas Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

Felix Fröhlich, Table of n, a(n) for n = 0..99
Alexander V. Kitaev, Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin, Symmetry, Integrability and Geometry: Methods and Applications, Vol. 15 (2019), 046, 53 pages; arXiv preprint, arXiv:1809.00122 [math.CA], 2018-2019.
Eric Weisstein's World of Mathematics, Cyclomatic Number.
Eric Weisstein's World of Mathematics, Sierpinski Tetrahedron Graph.
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A000051, A000120, A000225, A000302, A002001, A002063, A002193, A002450, A005057, A010503, A010532, A010541, A010767, A015521, A020988, A027637 (partial products), A078904 (partial sums), A079978, A080674, A164346 (first differences), A178789, A179857, A248721.

a024036 = (subtract 1) . a000302
a024036_list = iterate ((+ 3) . (* 4)) 0
-- Reinhard Zumkeller, Oct 03 2012

A024036:=n->4^n-1; seq(A024036(n), n=0..30); # Wesley Ivan Hurt, Apr 04 2014

Array[4^# - 1 &, 50, 0] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
(* Start from Eric W. Weisstein, Sep 19 2017 *)
Table[4^n - 1, {n, 0, 20}]
4^Range[0, 20] - 1
LinearRecurrence[{5, -4}, {0, 3}, 20]
CoefficientList[Series[3 x/(1 - 5 x + 4 x^2), {x, 0, 20}], x]
(* End *)

for(n=0, 100, print1(4^n-1, ", ")) \\ Felix Fröhlich, Jul 04 2014

[gaussian_binomial(2*n,1, 2) for n in range(21)] # Zerinvary Lajos, May 28 2009

[stirling_number2(2*n+1, 2) for n in range(21)] # Zerinvary Lajos, Nov 26 2009

a(n) = 3*A002450(n). - N. J. A. Sloane, Feb 19 2004
G.f.: 3*x/((-1+x)*(-1+4*x)) = 1/(-1+x) - 1/(-1+4*x). - R. J. Mathar, Nov 23 2007
E.g.f.: exp(4*x) - exp(x). - Mohammad K. Azarian, Jan 14 2009
a(n) = A000051(n)*A000225(n). - Reinhard Zumkeller, Feb 14 2009
A079978(a(n)) = 1. - Reinhard Zumkeller, Nov 22 2009
a(n) = A179857(A000225(n)), for n > 0; a(n) > A179857(m), for m < A000225(n). - Reinhard Zumkeller, Jul 31 2010
a(n) = 4*a(n-1) + 3, with a(0) = 0. - Vincenzo Librandi, Aug 01 2010
A000120(a(n)) = 2*n. - Reinhard Zumkeller, Feb 07 2011
a(n) = (3/2)*A020988(n). - Omar E. Pol, Mar 15 2012
a(n) = (Sum_{i=0..n} A002001(i)) - 1 = A178789(n+1) - 3. - Ivan N. Ianakiev, Nov 22 2013
a(n) = n*E(2*n-1,1)/B(2*n,1), for n > 0, where E(n,x) denotes the Euler polynomials and B(n,x) the Bernoulli polynomials. - Peter Luschny, Apr 04 2014
a(n) = A000302(n) - 1. - Sean A. Irvine, Jun 18 2019
Sum_{n>=1} 1/a(n) = A248721. - Amiram Eldar, Nov 13 2020
a(n) = A080674(n) - A002450(n). - Elmo R. Oliveira, Dec 02 2023

More terms Wesley Ivan Hurt, Apr 04 2014

A379388 Decimal expansion of the midradius of a deltoidal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

2, 7, 0, 3, 4, 4, 4, 1, 8, 5, 3, 7, 4, 8, 6, 3, 3, 0, 2, 6, 6, 5, 9, 6, 2, 8, 8, 4, 6, 7, 5, 3, 2, 9, 5, 5, 3, 0, 3, 6, 4, 0, 1, 9, 3, 3, 7, 4, 7, 4, 9, 1, 7, 2, 0, 7, 7, 6, 0, 8, 3, 2, 0, 9, 5, 1, 6, 8, 3, 8, 6, 0, 1, 6, 6, 4, 5, 7, 3, 1, 8, 4, 6, 1, 9, 3, 6, 9, 3, 6

Offset: 1

Paolo Xausa, Dec 23 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			2.70344418537486330266596288467532955303640193...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.
Wikipedia, Deltoidal hexecontahedron.
Index entries for algebraic numbers, degree 2.

Cf. A379385 (surface area), A379386 (volume), A379387 (inradius), A379389 (dihedral angle).
Cf. A377795 (midradius of a (small) rhombicosidodecahedron with unit edge length).
Cf. A010532.

First[RealDigits[5/4 + 13/Sqrt[80], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "Midradius"], 10, 100]]

5/4 + 13/(4*sqrt(5)) \\ Charles R Greathouse IV, Feb 05 2025

Equals 5/4 + 13/(4*sqrt(5)) = 5/4 + 13/A010532.

A086466 Decimal expansion of 2*sqrt(5)/5 arccsch(2).

Original entry on oeis.org

4, 3, 0, 4, 0, 8, 9, 4, 0, 9, 6, 4, 0, 0, 4, 0, 3, 8, 8, 8, 9, 4, 3, 3, 2, 3, 2, 9, 5, 0, 6, 0, 5, 4, 2, 5, 4, 2, 4, 5, 7, 0, 6, 8, 2, 5, 4, 0, 2, 8, 9, 6, 5, 4, 7, 5, 7, 0, 0, 6, 1, 0, 3, 9, 9, 2, 5, 6, 1, 2, 1, 5, 4, 6, 1, 1, 3, 1, 9, 6, 1, 3, 6, 1, 4, 9, 0, 2, 6, 4, 6, 9, 7, 2, 1, 9, 9, 5, 5, 4, 0, 6

Offset: 0

Eric W. Weisstein, Jul 21 2003

Equals the value of the Dirichlet L-series of the non-principal character modulo 5 (A080891) at s=1. - Jianing Song, Nov 16 2019

			0.43040894096400403888943323295060542542457...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.2, p. 7.

R. J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, Table 22 for L(m=5,r=3,s=1).
H.-J. Seiffert, Problem B-771, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 32, No. 4 (1994), p. 374; More Sums, Solution to Problem B-771 by Don Redmond, ibid., Vol. 33, No. 5 (1995), pp. 470-471.
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27
Eric Weisstein's World of Mathematics, Central Binomial Coefficient.
Index entries for transcendental numbers

Cf. A086465, A086467, A086468.

Cf. A000032, A000045, A080891, A328717 (s=2), A344041.

2*Log[GoldenRatio]/Sqrt[5] // RealDigits[#, 10, 102]& // First (* Jean-François Alcover, Apr 18 2014 *)

2*log((1+sqrt(5))/2)/sqrt(5) \\ Stefano Spezia, Oct 15 2024

Equals Sum_{k>=1} (-1)^(k-1)/(k*binomial(2*k,k)).
Equals A010532 * A002390 / 10. - R. J. Mathar, Jul 26 2010
Also equals f'(0) = 2*log(phi)/sqrt(5), with f(x) = (phi^x-cos(Pi*x)*phi^-x)/sqrt(5), the real Fibonacci interpolating function. - Jean-François Alcover, Apr 04 2014
Equals Sum_{k>=1} A080891(k)/k = Sum_{k>=1} Kronecker(5,k)/k = 1 - 1/2 - 1/3 + 1/4 + 1/6 - 1/7 - 1/8 + 1/9 + ... - Jianing Song, Nov 16 2019
Equals Sum_{k>=1} F(k)/(k*2^(k+1)), where F(k) is the k-th Fibonacci number (A000045). - Amiram Eldar, Aug 10 2020
Sum_{k>=1} (2*k+1)*Lucas(k)/(k*(k+1)*2^k) = 10*c + 2 = 6.3040894096... where c is this constant (Seiffert, 1994). - Amiram Eldar, Jan 15 2022
Equals Sum_{k>=1} F(k)/(k*3^k), where F(k) is the k-th Fibonacci number (A000045). - Amiram Eldar, Jul 02 2023
Equals 1/Product_{p prime} (1 - Kronecker(5,p)/p), where Kronecker(5,p) = 0 if p = 5, 1 if p == 1 or 4 (mod 5) or -1 if p == 2 or 3 (mod 5). - Amiram Eldar, Dec 17 2023
Equals A344041/2. - Hugo Pfoertner, Oct 16 2024

A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

Original entry on oeis.org

9, 0, 7, 3, 3, 3, 3, 1, 9, 3, 8, 8, 0, 1, 8, 7, 9, 9, 3, 1, 4, 9, 9, 8, 3, 9, 8, 1, 0, 1, 8, 1, 6, 2, 7, 2, 2, 1, 5, 3, 1, 3, 3, 9, 3, 0, 6, 0, 3, 6, 7, 3, 4, 9, 2, 1, 4, 7, 6, 4, 2, 4, 5, 8, 5, 0, 3, 7, 6, 6, 8, 7, 2, 0, 6, 1, 5, 5, 3, 5, 4, 0, 3, 6, 2, 6, 2, 2, 8, 0

Offset: 1

Paolo Xausa, May 26 2025

The gyroelongated pentagonal cupola is Johnson solid J_24.

			9.07333319388018799314998398101816272215313393060...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated pentagonal cupola.
Index entries for algebraic numbers, degree 8

Cf. A384284 (surface area).

Cf. A002163, A010532, A179590, A179639, A179641, A384138, A384140, A384144, A384213.

First[RealDigits[(5 + Sqrt[80] + 5*Sqrt[2*(Sqrt[650 + 290*Sqrt[5]] - Sqrt[5] - 1)])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J24", "Volume"], 10, 100]]

(5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 \\ Charles R Greathouse IV, Aug 19 2025

Equals (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (5 + A010532 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 1679616*x^8 - 11197440*x^7 + 27060480*x^6 + 35769600*x^5 - 4456749600*x^4 - 10714248000*x^3 + 3828402000*x^2 + 13859430000*x + 5340175625.

A378976 Decimal expansion of the midradius of a triakis icosahedron with unit shorter edge length.

Original entry on oeis.org

1, 3, 9, 4, 4, 2, 7, 1, 9, 0, 9, 9, 9, 9, 1, 5, 8, 7, 8, 5, 6, 3, 6, 6, 9, 4, 6, 7, 4, 9, 2, 5, 1, 0, 4, 9, 4, 1, 7, 6, 2, 4, 7, 3, 4, 3, 8, 4, 4, 6, 1, 0, 2, 8, 9, 7, 0, 8, 3, 5, 8, 8, 9, 8, 1, 6, 4, 2, 0, 8, 3, 7, 0, 2, 5, 5, 1, 2, 1, 9, 5, 9, 7, 6, 5, 7, 6, 5, 7, 6

Offset: 1

Paolo Xausa, Dec 14 2024

The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.

			1.3944271909999158785636694674925104941762473438446...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triakis Icosahedron.
Wikipedia, Triakis icosahedron.

Cf. A378973 (surface area), A378974 (volume), A378975 (inradius), A378977 (dihedral angle).
Cf. A377697 (midradius of a truncated dodecahedron with unit edge length).
Cf. A002163, A010532, A249600.

First[RealDigits[1/2 + 2/Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Midradius"], 10, 100]]

Equals 1/2 + 2/sqrt(5) = 1/2 + 2/A002163.

Equals (A249600 + 13)/10 = (A010532 + 5)/10.

A384624 Decimal expansion of the volume of a pentagonal orthobicupola with unit edge.

Original entry on oeis.org

4, 6, 4, 8, 0, 9, 0, 6, 3, 6, 6, 6, 6, 3, 8, 6, 2, 6, 1, 8, 7, 8, 8, 9, 8, 2, 2, 4, 9, 7, 5, 0, 3, 4, 9, 8, 0, 5, 8, 7, 4, 9, 1, 1, 4, 6, 1, 4, 8, 7, 0, 0, 9, 6, 5, 6, 9, 4, 5, 2, 9, 6, 6, 0, 5, 4, 7, 3, 6, 1, 2, 3, 4, 1, 8, 3, 7, 3, 9, 8, 6, 5, 8, 8, 5, 8, 8, 5, 8, 7

Offset: 1

Paolo Xausa, Jun 05 2025

The pentagonal orthobicupola is Johnson solid J_30.

Also the volume of a pentagonal gyrobicupola (Johnson solid J_31) with unit edge.

			4.6480906366663862618788982249750349805874911461487...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal orthobicupola.
Wikipedia, Pentagonal gyrobicupola.

Cf. A384625 (surface area).

Cf. A010532, A384287.

First[RealDigits[(5 + Sqrt[80])/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "Volume"], 10, 100]]

Equals (5 + 4*sqrt(5))/3 = (5 + A010532)/3.

Equals the largest root of 9*x^2 - 30*x - 55.

A214986 Power ceiling array for the golden ratio, by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 7, 8, 5, 1, 1, 12, 21, 22, 7, 1, 1, 20, 55, 94, 48, 12, 1, 1, 33, 144, 399, 329, 134, 18, 1, 1, 54, 377, 1691, 2255, 1487, 323, 30, 1, 1, 88, 987, 7164, 15456, 16492, 5796, 872, 47, 1, 1, 143, 2584, 30348, 105937, 182900

Offset: 1

Clark Kimberling, Oct 28 2012

row 0: A000012 ... row 6: A049660
row 1: A000071 ... row 8: A049668
row 2: A001906 ... col 0: A000012
row 3: A049652 ... col 1: A169986
row 4: A004187
For x>1, define c(x,0) = 1 and c(x,n) = ceiling(x*c(x,n-1)) for n>0.  Row m of A214986 is the sequence c(r^m,n), where r = golden ratio = (1 + sqrt(5))/2.  The name of the array corresponds to the power ceiling function f(x) = limit of c(x,n)/x^n as n increases without bound; f(x) generalizes the case for x = 3/2 as described under "Power Ceilings" at MathWorld.  For a graph of f(x), see the Mathematica program at A083286.
The term "power ceiling sequence" extends to sequences generated by recurrences P(n) = ceiling(x*P(n-1)) + g(n), and "power ceiling functions" f(x) to the limit of P(n)/x^n in case x>1 and g(n)/x^n -> 0.
Suppose that h is a nonnegative integer and g(n) is a constant.  If x is a positive integer power of the golden ratio r, then f(x), in many cases, lies in the field Q(sqrt(5)).  Examples matching rows of A214986, using g(n) = 0, follow:
...
x ... P ........ f(x)
r ... A000071 .. (5 + 2*sqrt(5))/2 = 1.8944... (A010532)
r^2 . A001906 .. (5 + 3*sqrt(5))/10 = 1.7082...(A176015)
r^3 . A049652 .. (25 + 11*sqrt(5))/40 = 1.2399...
r^4 . A004187 .. (15 + 7*sqrt(5))/10 = 1.0219...
...
If k is odd, then f(r^k) = r^k((b(k) + c(k))/d(k)), where
b(k) = L(j)^2 + L(j-1)^2, where j=[(k+1)/2], L=A000032 (Lucas numbers); c(k) = (L(k)+2)*sqrt(5); d(k) = 10*F(k)*L(k), where F=A000045 (Fibonacci numbers).  If k is even, then f(r^k) = r^k/(F(k)*sqrt(5)).

			Northwest corner:
1...1....1.....1......1.......1
1...2....4.....7......12......20
1...3....8.....21.....55......144
1...5....22....94.....399.....1691
1...7....48....329....2255....15456
1...19...134...1487...16492...182900

Clark Kimberling, Antidiagonals n = 1..35, flattened
Eric Weisstein's World of Mathematics, Power Ceilings

Cf. A000045, A214978, A214984, A214987.

r = GoldenRatio;
s[x_, 0] := 1; s[x_, n_] := Ceiling[x*s[x, n - 1]];
t = TableForm[Table[s[r^m, n], {m, 0, 10}, {n, 0, 10}]  ]
u = Flatten[Table[s[r^m, n - m], {n, 0, 10}, {m, 0, n}]]

The odd-numbered rows of A214986 are even-numbered rows of A213978; the even-numbered rows of A214986 are odd-numbered rows of A214984.

A384144 Decimal expansion of the volume of an elongated pentagonal cupola with unit edge.

Original entry on oeis.org

1, 0, 0, 1, 8, 2, 5, 4, 1, 6, 1, 2, 7, 1, 3, 2, 6, 6, 3, 7, 3, 6, 5, 1, 7, 5, 5, 5, 2, 5, 7, 9, 7, 9, 2, 0, 5, 0, 3, 1, 0, 5, 0, 0, 9, 3, 1, 9, 1, 8, 8, 3, 1, 5, 5, 0, 4, 4, 5, 1, 5, 5, 4, 5, 6, 2, 1, 0, 8, 3, 8, 8, 3, 8, 3, 2, 9, 5, 9, 7, 2, 2, 9, 0, 7, 9, 4, 2, 7, 2

Offset: 2

Paolo Xausa, May 22 2025

The elongated pentagonal cupola is Johnson solid J_20.

			10.0182541612713266373651755525797920503105009319...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Elongated pentagonal cupola.

Cf. A179591 (surface area - 10).

Cf. A010476, A010532, A384138, A384140, A384213.

First[RealDigits[(5 + Sqrt[80] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J20", "Volume"], 10, 100]]

Equals (5 + 4*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (5 + A010532 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 324*x^4 - 1080*x^3 - 20340*x^2 - 18600*x + 49975.

A040071 Continued fraction for sqrt(80).

Original entry on oeis.org

8, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1

Offset: 0

N. J. A. Sloane

			8.9442719099991587856366946... = 8 + 1/(1 + 1/(16 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 09 2009

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for continued fractions for constants.
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010532 (decimal expansion).

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[80],300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
PadRight[{8},120,{16,1}] (* Harvey P. Dale, Apr 16 2022 *)

{ allocatemem(932245000); default(realprecision, 26000); x=contfrac(sqrt(80)); for (n=0, 20000, write("b040071.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

a(n) = 4^(1+(-1)^n) for n>0, a(0)=8. - Bruno Berselli, Dec 29 2015
From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(2^e) = 16, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 15/2^s). (End)

cp's OEIS Frontend

A248304 Egyptian fraction representation of sqrt(80) (A010532) using a greedy function.

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A024036 a(n) = 4^n - 1.

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A379388 Decimal expansion of the midradius of a deltoidal hexecontahedron with unit shorter edge length.

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A086466 Decimal expansion of 2*sqrt(5)/5 arccsch(2).

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A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

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A378976 Decimal expansion of the midradius of a triakis icosahedron with unit shorter edge length.

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A384624 Decimal expansion of the volume of a pentagonal orthobicupola with unit edge.

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