Irrationality Sequence
المؤلف:
Guy, R. K.
المصدر:
"Irrationality Sequence." §E24 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
24-7-2020
880
Irrationality Sequence
A sequence of positive integers ![<span style=]()
{a_n}" src="https://mathworld.wolfram.com/images/equations/IrrationalitySequence/Inline1.gif" style="height:15px; width:23px" /> such that 
is irrational for all integer sequences ![<span style=]()
{b_n}" src="https://mathworld.wolfram.com/images/equations/IrrationalitySequence/Inline3.gif" style="height:15px; width:23px" />. Erdős showed that ![<span style=]()
{2^(2^n)}={1,2,4,16,256,...}" src="https://mathworld.wolfram.com/images/equations/IrrationalitySequence/Inline4.gif" style="height:22px; width:166px" /> (OEIS A001146) is an irrationality sequence.
REFERENCES:
Guy, R. K. "Irrationality Sequence." §E24 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 225, 1994.
Sloane, N. J. A. Sequence A001146/M1297 in "The On-Line Encyclopedia of Integer Sequences."
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