A010767 - OEIS

A010767

Decimal expansion of 4th root of 2.

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

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OFFSET

1,3

COMMENTS

An algebraic integer of degree 4. - Charles R Greathouse IV, Nov 12 2014

REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.23, p. 407.

LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..20001 (first 1000 digits from Vincenzo Librandi).

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.

Simon Plouffe, 2^(1/4) or sqrt(sqrt(2)) to 20000 digits.

Simon Plouffe, 2^(1/4) to 1024 places.

Nikita Sidorov and Boris Solomyak, On the topology of sums in powers of an algebraic number, arXiv:0909.3324 [math.NT], 2009-2011.

David Terr and Eric W. Weisstein, Pisot Number.

Eric Weisstein's World of Mathematics, Algebraic integer.

Index entries for algebraic numbers, degree 4.

FORMULA

Equals Product_{k>=0} (1 + (-1)^k/(4*k + 3)). - Amiram Eldar, Jul 25 2020

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

Conjecture: Equals Sum_{k>=0} A007096(k) / exp(k*Pi). - Simon Plouffe, Sep 09 2025

EXAMPLE

1.189207115002721066717499970560475915292972092...