A072449 -id:A072449 - cp's OEIS frontend

A257574 Continued square root map applied to the sequence of positive even numbers, (2, 4, 6, 8, ...).

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

Offset: 1

N. J. A. Sloane, May 02 2015

The continued square root or CSR map applied to a sequence b = (b(1), b(2), b(3), ...) is the number CSR(b) := sqrt(b(1)+sqrt(b(2)+sqrt(b(3)+sqrt(b(4)+...)))).

Taking out a factor sqrt(2), one gets CSR(2, 4, 6, 8, ...) = sqrt(2) CSR(1, 1, 3/8, 1/32, ...) < A002193*A001622 = (sqrt(5)+1)/sqrt(2). - M. F. Hasler, May 01 2018

			sqrt(2 + sqrt(4 + sqrt(6 + sqrt(8 + ...)))) = 2.1584768723110397656558534...

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..400
A. Herschfeld, On Infinite Radicals, Amer. Math. Monthly, 42 (1935), 419-429.
Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.

Cf. A072449, A257575..A257581, A105817, A099879, A001622, A105546.

(CSR(v,s)=forstep(i=#v,1,-1,s=sqrt(v[i]+s));s); t=0;for(N=5,oo,(t==t=Str(CSR([1..2*N]*2)))&&break;print(2*N": "t)) \\ Allows to see the convergence, which is reached when length of vector ~ precision [given as number of digits]. Using Str() to avoid infinite loop when internal representation is "fluctuating". - M. F. Hasler, May 04 2018

a(27)-a(87) from Hiroaki Yamanouchi, May 03 2015

Edited by M. F. Hasler, May 01 2018

A105546 Decimal expansion of prime nested radical.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Apr 12 2005

sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ...)))) = 1.75793275661800...
"It was discovered by T. Vijayaraghavan that the infinite radical, sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ... )))) where a_n >= 0, will converge to a limit if and only if the limit of log(a_n)/2^n exists." [Clawson, 229; cf. A072449].
We know the asymptotic limit of primes and hence that the Prime Nested Radical converges.
Clawson misstates Vijayaraghavan's theorem. Vijayaraghavan proved that for a_n > 0, the infinite radical sqrt(a_1 + sqrt(a_2 + sqrt(a_3 + ...))) converges if and only if limsup (log a_n)/2^n < infinity. (For example, suppose a_n = 1 if n is odd, and a_n = e^2^n if n is even. Then (log a_n)/2^n = 0, 1, 0, 1, 0, 1, ... for n >= 1, so the limit does not exist. However, limsup (log a_n)/2^n = 1 and the infinite radical converges.) - Jonathan Sondow, Mar 25 2014

			2.10359749633989726261993964968532544404216228824001387298687284563...

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 and 229.
S. R. Finch, Analysis of a Radical Expansion, Section 1.2.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, p. 8, 2003.

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Jonathan M. Borwein and G. de Barra, Nested Radicals, Amer. Math. Monthly 98, 735-739, 1991.
Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl., 332 (2007), 292-314; see pp. 305-306.
Eric Weisstein's World of Mathematics, Nested Radical Constant.
Wikipedia, Tirukkannapuram Vijayaraghavan

Cf. A000040, A072449, A239349.
A105548 is the continued fraction representation of this prime nested radical.
A105815 is the similar semiprime nested radical.
A105817 is the Fibonacci nested radical.

RealDigits[Fold[Sqrt[#1 + #2] &, 0, Reverse[Prime[Range[ 80]]]], 10, 111][[1]] (* Robert G. Wilson v, May 31 2005 *)

sqrt(2 + sqrt(3 + sqrt(5 + sqrt(7 + sqrt(11 + ... + sqrt(prime(n) + ...)))).

Crossrefs corrected by Jaroslav Krizek, Jan 03 2015

A099874 Decimal expansion of a nested radical: CubeRoot(1 + CubeRoot(2 + CubeRoot(3 + CubeRoot(4 + ...

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

			1.365300948604002967552742168986737...

Cf. A072449 for version using square root rather than cube root.

RealDigits[ Fold[(#1 + #2)^(1/3) &, 0, Reverse[Range[100]]], 10, 111][[1]]

t=0; forstep(n=200,1,-1,t=(t+n)^(1/3)); t

A099876 Decimal expansion of a nested radical: sqrt(1! + sqrt(2! + sqrt(3! + ...

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

			1.82701471760859222637384319285...

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), The CSR Function, Vol. 4 (No. 34, Jan 1976), pages PC34-10 to PC34-11. Annotated and scanned copy.

Cf. A072449, A099874.

RealDigits[Fold[Sqrt[#1 + #2] &, 0, Reverse[Range[100]!]], 10, 111][[1]]

t=0; forstep(n=300,1,-1,t=sqrt(t+n!)); t \\ gives more than enough correct digits for the number given here.

A099879 Decimal expansion of a nested radical: sqrt(1^2 + sqrt(2^2 + sqrt(3^2 + ...

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 03 2004

			1.94265542276398732822141329141266723768807363...

Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.

Cf. A072449, A099874, A099876 to A099878 for other nested radicals.

k = 64; r = 65; While[k > 0, r = Sqrt[k^2 + r]; k-- ]; RealDigits[r, 10, 111][[1]] (* Robert G. Wilson v, Nov 04 2004 *)

t=0; forstep(n=100,1,-1,t=sqrt(t+n^2)); print(t)

\\ We need about b/log(b) steps, where epsilon = 2^-b.
my(b=bitprecision(1.),t); forstep(n=b\log(b)+9,1,-1, t=sqrt(t+n^2)); t \\ Charles R Greathouse IV, Aug 19 2025

A105817 Decimal expansion of the Fibonacci nested radical.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Apr 21 2005

The continued fraction expression of this is A105818. "It was discovered by T. Vijayaraghavan that the infinite radical, sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ... where a_n => 0, will converge to a limit if and only if the limit of (ln a_n)/2^n exists." [Clawson, 229; Sloane]. We know the asymptotic limit of Fibonacci numbers is Phi^n (Binet expansion) and that Phi^n < 2^n and hence that the Fibonacci Nested Radical converges.

Clawson misstates Vijayaraghavan's theorem. Vijayaraghavan proved that for a_n > 0, the infinite radical sqrt(a_1 + sqrt(a_2 + sqrt(a_3 + ...))) converges if and only if limsup (log a_n)/2^n < infinity. (For example, suppose a_n = 1 if n is odd, and a_n = e^2^n if n is even. Then (log a_n)/2^n = 0, 1, 0, 1, 0, 1, ... for n >= 1, so the limit does not exist. However, limsup (log a_n)/2^n = 1 and the infinite radical converges.) - Jonathan Sondow, Mar 25 2014

			1.66198246232781155796760608181513129505616756246503500829906806743...

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.
S. R. Finch, "Analysis of a Radical Expansion." Section 1.2.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, p. 8, 2003.

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Jonathan M. Borwein and G. de Barra, Nested Radicals, Amer. Math. Monthly 98, 735-739, 1991.
Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl., 332 (2007), 292-314; see pp. 305-306.
Eric Weisstein's World of Mathematics, Nested Radical Constant.
Wikipedia, Tirukkannapuram Vijayaraghavan

Cf. A000045; A072449, A083869, A099874, A099876, A099877, A099878, A099879, A105546, A105548, A105815, A105816, A105818, A239349 for other nested radicals.

Cf. A151558.

RealDigits[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Fibonacci[ Range[50]]]], 10, 111][[1]] (* Robert G. Wilson v, Apr 21 2005 *)

Sqrt(1 + sqrt(1 + sqrt(2 + sqrt(3 + sqrt(5 + ... + sqrt(Fibonacci(n)=A000045)))).

A099877 Decimal expansion of nested radical: Sqrt(1^2 + CubeRoot(2^3 + 4thRoot(3^4 + 5thRoot(4^5 + ...

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

			1.7962268369357180316400150423265975895...

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A072449, A099874, A099876.

t=0:forstep(n=100,1,-1,t=(t+n^(n+1))^(1/(n+1)))

A105815 Decimal expansion of the semiprime nested radical.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Apr 21 2005

The semiprime nested radical is defined by the infinite recursion: sqrt(4 + sqrt(6 + sqrt(9 + sqrt(10 + sqrt(14 + ... + sqrt(semiprime(n))))). This converges by the criterion of T. Vijayaraghavan that "the infinite radical, sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ... where a_n => 0, will converge to a limit if and only if the limit of (ln a_n)/2^n exists." [Clawson, 229; Sloane A072449]. The continued fraction representation of this constant is A105816.

Clawson misstates Vijayaraghavan's theorem. Vijayaraghavan proved that for a_n > 0, the infinite radical sqrt(a_1 + sqrt(a_2 + sqrt(a_3 + ...))) converges if and only if limsup (log a_n)/2^n < infinity. (For example, suppose a_n = 1 if n is odd, and a_n = e^2^n if n is even. Then (log a_n)/2^n = 0, 1, 0, 1, 0, 1, ... for n >= 1, so the limit does not exist. However, limsup (log a_n)/2^n = 1 and the infinite radical converges.) - Jonathan Sondow, Mar 25 2014

			2.66352563480685654498944673272195514599922982689272932914833705868...

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.
Steven R. Finch, Analysis of a Radical Expansion, Section 1.2.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, 2003, p. 8.

Jonathan M. Borwein and G. de Barra, Nested Radicals, Amer. Math. Monthly 98, 735-739, 1991.
Jonathan Sondow and Petros Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl., 332 (2007), 292-314; see pp. 305-306.
Eric Weisstein's World of Mathematics, Nested Radical Constant.
Wikipedia, Tirukkannapuram Vijayaraghavan.

For other nested radicals, see A072449, A083869, A099874, A099876, A099877, A099878, A099879, A105546, A105548, A105816, A239349.

Cf. A001358.

fQ[n_] := Plus @@ Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]] == 2; RealDigits[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Select[ Range[260], fQ[ # ] &]]], 10, 111][[1]] (* Robert G. Wilson v, May 31 2005 *)

Limit_{n -> infinity} sqrt(4 + sqrt(6 + sqrt(9 + sqrt(10 + sqrt(14 + ... + sqrt(semiprime(n))))), where semiprime(n) = A001358(n).

A099878 Decimal expansion of a nested radical: Sqrt(1 + CubeRoot(2 + 4thRoot(3 + 5thRoot(4 + ...

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 03 2004

			1.58454170990556500250912545055...

Cf. A072449, A099874, A099876, A099877 for other nested radicals.

k = 43; r = 44; While[k > 0, r = (k + r)^(1/(k + 1)); k-- ]; RealDigits[r, 10, 111][[1]] (* Robert G. Wilson v, Nov 04 2004 *)

t=0;forstep(n=100,1,-1,t=(t+n)^(1/(n+1)));print(t)

A105548 Continued fraction expansion of prime nested radical A105546.

Original entry on oeis.org

2, 9, 1, 1, 1, 7, 3, 5, 4, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 15, 1, 3, 1, 41, 6, 1, 3, 1, 3, 10, 1, 1, 1, 9, 9, 1, 25, 1, 3, 1, 1, 2, 2, 2, 1, 34, 59, 2, 2, 2, 1, 2, 2, 3, 3, 1, 5, 2, 21, 3, 4, 10, 1, 3, 20, 2, 3, 2, 1, 4, 7, 1, 6, 1, 6, 3, 4, 1, 3, 5, 6, 1, 1, 4, 1, 3, 6, 25, 7, 2, 1, 1, 2, 1, 6, 1, 1, 7, 1, 3, 2

Offset: 0

Jonathan Vos Post, Apr 14 2005

Records are: 9,15,41,59,117,153,599,1663,8212,..., . Robert G. Wilson v: "It would appear superficially that this constant is normal." Sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... = ~ 1.75793275661800... "It was discovered by T. Vijayaraghavan that the infinite radical, sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ... where a_n => 0, will converge to a limit if and only if the limit of (ln a_n)/2^n exists." [Clawson, 229; A072449] We know the asymptotic limit of primes and hence that the Prime Nested Radical converges.

Clawson misstates Vijayaraghavan's theorem. Vijayaraghavan proved that for a_n > 0, the infinite radical sqrt(a_1 + sqrt(a_2 + sqrt(a_3 + ...))) converges if and only if limsup (log a_n)/2^n < infinity. (For example, suppose a_n = 1 if n is odd, and a_n = e^2^n if n is even. Then (log a_n)/2^n = 0, 1, 0, 1, 0, 1, ... for n >= 1, so the limit does not exist. However, limsup (log a_n)/2^n = 1 and the infinite radical converges.) - Jonathan Sondow, Mar 25 2014

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.

Jonathan M. Borwein and G. de Barra, Nested Radicals, Amer. Math. Monthly 98, 735-739, 1991.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl., 332 (2007), 292-314; see pp. 305-306.
Eric Weisstein's World of Mathematics, Nested Radical Constant.
Wikipedia, Tirukkannapuram Vijayaraghavan

Cf. A000040, A072449, A105546, A239349.

f[n_] := Block[{k = n, s = 0}, While[k > 0, s = Sqrt[s + k]; k-- ]; s]; ContinuedFraction[ f[100], 101]; (* Robert G. Wilson v *)

Continued fraction expansion of sqrt(2 + sqrt(3 + sqrt(5 + sqrt(7 + sqrt(11 + ... + sqrt(prime(n))))).

Offset changed by Andrew Howroyd, Aug 03 2024

cp's OEIS Frontend

A257574 Continued square root map applied to the sequence of positive even numbers, (2, 4, 6, 8, ...).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

A105546 Decimal expansion of prime nested radical.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A099874 Decimal expansion of a nested radical: CubeRoot(1 + CubeRoot(2 + CubeRoot(3 + CubeRoot(4 + ...

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

A099876 Decimal expansion of a nested radical: sqrt(1! + sqrt(2! + sqrt(3! + ...

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A099879 Decimal expansion of a nested radical: sqrt(1^2 + sqrt(2^2 + sqrt(3^2 + ...

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

A105817 Decimal expansion of the Fibonacci nested radical.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A099877 Decimal expansion of nested radical: Sqrt(1^2 + CubeRoot(2^3 + 4thRoot(3^4 + 5thRoot(4^5 + ...

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

A105815 Decimal expansion of the semiprime nested radical.

Views

Author

Keywords