A005533 Decimal expansion of fifth root of 4. (Formerly M2231)

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

Offset

1,2

References

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Jean-Paul Allouche, Henri Cohen, Michel Mendès France, and Jeffrey O. Shallit, De nouveaux curieux produits infinis, Acta Arithmetica, Vol. 49, No. 2 (1987), pp. 141-153; alternative link.

Formula

Equals Product_{k>=0} ((2*k+2)/(2*k+1))^((-3/2)^A000120(k)) (Allouche et al., 1987). - Amiram Eldar, Feb 04 2024

Example

1.319507910772894259374001971229640133033469013193418681505807795980535... - Harry J. Smith, May 11 2009

Mathematica

RealDigits[N[4^(1/5), 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

Prog

(PARI) { default(realprecision, 20080); x=4^(1/5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005533.txt", n, " ", d)); } \\ Harry J. Smith, May 11 2009

Crossrefs

Cf. A000120, A003118 (continued fraction).

Sequence in context: A091579 A136159 A371746 * A331257 A112626 A050155

Adjacent sequences: A005530 A005531 A005532 * A005534 A005535 A005536

Keyword

cons,nonn

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 11 2018

Status

approved