

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
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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=(xd)*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



