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A309948 Decimal expansion of the real part of the square root of 1 + i. 3
1, 0, 9, 8, 6, 8, 4, 1, 1, 3, 4, 6, 7, 8, 0, 9, 9, 6, 6, 0, 3, 9, 8, 0, 1, 1, 9, 5, 2, 4, 0, 6, 7, 8, 3, 7, 8, 5, 4, 4, 3, 9, 3, 1, 2, 0, 9, 2, 7, 1, 5, 7, 7, 4, 3, 7, 4, 4, 4, 1, 1, 5, 7, 8, 8, 4, 2, 8, 7, 5, 0, 5, 3, 5, 5, 5, 2, 8, 4, 8, 1, 1, 1, 3, 6, 5, 3, 6, 0, 6, 6, 3, 5, 6, 4, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

i is the imaginary unit such that i^2 = -1.

Also imaginary part of sqrt(-1 + i).

LINKS

Table of n, a(n) for n=1..96.

FORMULA

Re(sqrt(1 + i)) = sqrt(1/2 + 1/sqrt(2)) = 2^(1/4) * cos(Pi/8).

Equals Im(-sqrt(-1 - i)). - Peter Luschny, Sep 20 2019

EXAMPLE

Re(sqrt(1 + i)) = 1.09868411346780996603980119524...

MAPLE

Digits := 120: Im(-sqrt(-1 - I))*10^95:

ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 20 2019

MATHEMATICA

RealDigits[Sqrt[1/2 + 1/Sqrt[2]], 10, 100][[1]]

PROG

(PARI) real(sqrt(1+I)) \\ Michel Marcus, Sep 16 2019

CROSSREFS

Cf. A309949 (imaginary part).

Sequence in context: A155920 A082124 A132721 * A086053 A129269 A094145

Adjacent sequences:  A309945 A309946 A309947 * A309949 A309950 A309951

KEYWORD

nonn,cons,easy

AUTHOR

Alonso del Arte, Aug 24 2019

STATUS

approved

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Last modified July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)