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A042972 Decimal expansion of i^(-i), where i = sqrt(-1). 6
4, 8, 1, 0, 4, 7, 7, 3, 8, 0, 9, 6, 5, 3, 5, 1, 6, 5, 5, 4, 7, 3, 0, 3, 5, 6, 6, 6, 7, 0, 3, 8, 3, 3, 1, 2, 6, 3, 9, 0, 1, 7, 0, 8, 7, 4, 6, 6, 4, 5, 3, 4, 9, 4, 0, 0, 2, 0, 8, 1, 5, 4, 8, 9, 2, 4, 2, 5, 5, 1, 9, 0, 4, 8, 9, 1, 5, 8, 2, 1, 3, 6, 7, 4, 8, 7, 0, 4, 7, 6, 6, 5, 8, 3, 8, 8, 3, 3, 5, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Square root of Gelfond's constant (A039661). Since Gelfond's constant e^Pi is transcendental, e^(Pi/2) is transcendental. - Daniel Forgues, Apr 15 2011

The complex sequence (...((((i)^i)^i)^i)^...) (n pairs of brackets) is periodic with period 4 and the first four entries are i, e^(-Pi/2), -i, e^(+Pi/2). See A049006 for e^(-Pi/2). - Wolfdieter Lang, Apr 27 2013

A solution of x^i + x^(-i) = 0. In fact, x = Exp(Pi/2 + k*Pi), where k is any integer. - Robert G. Wilson v, Feb 04 2014

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

FORMULA

i^(-i) = i^(1/i) = e^(Pi/2).

Also (((i)^i)^i)^i. See a comment above on such powers. - Wolfdieter Lang, Apr 27 2013

EXAMPLE

=4.81047738096535165547303566670383312639017087466453494002081548924255190...

MATHEMATICA

RealDigits[Re[I^(1/I)], 10, 100][[1]] (* Alonso del Arte, Oct 31 2011 *)

RealDigits[ Exp[Pi/2], 10, 111][[1]] (* Robert G. Wilson v, Apr 08 2014 *)

PROG

(PARI) { default(realprecision, 10100); x=exp(1)^(Pi/2); for (n=1, 10000, d=floor(x); x=(x-d)*10; write("b042972.txt", n, " ", d)); } \\ Nathaniel Johnston, Apr 15 2011

CROSSREFS

Cf. A049006.

Sequence in context: A013328 A143462 A190966 * A021875 A200356 A127734

Adjacent sequences:  A042969 A042970 A042971 * A042973 A042974 A042975

KEYWORD

cons,nonn

AUTHOR

Marvin Ray Burns

EXTENSIONS

a(100) corrected by Nathaniel Johnston, Apr 15 2011

STATUS

approved

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Last modified October 30 07:54 EDT 2014. Contains 248796 sequences.