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A336774 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 differs from the exact value n^a(n), when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.

%I A336774 #14 Aug 06 2020 03:57:05
%S A336774 128,16,64,11,16,9,43,8,11,7,16,7,9,7,32,6,8,6,11,6,7,6,16,6,7,6,9,5,
%T A336774 7,5,26,5,6,5,8,5,6,5,11,5,6,5,7,5,6,5,16,5,6,5,7,5,6,5,9,5,5,5,7,5,5,
%U A336774 5,22,4,5,4,6,4,5,4,8,4,5,4,6,4,5,4,11,4,5,4
%N A336774 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 differs from the exact value n^a(n), when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.
%C A336774 For n a power of two the first deviation is caused by exceeding the maximum representable number of the binary32 single precision floating point format.
%H A336774 Hugo Pfoertner, <a href="/A336774/b336774.txt">Table of n, a(n) for n = 2..16384</a>
%H A336774 Hugo Pfoertner, <a href="/A336774/a336774.txt">Comparison with exact results</a>, range n=2..128, computed on x86-64 architecture.
%H A336774 Edmund Weitz, <a href="http://weitz.de/ieee/">IEEE 754 Calculator</a>, uses JavaScript (2016).
%H A336774 Wikipedia, <a href="https://en.wikipedia.org/wiki/IEEE_754">IEEE 754</a>.
%Y A336774 Cf. A336775, A336778, A336779.
%K A336774 nonn,fini
%O A336774 2,1
%A A336774 _Hugo Pfoertner_, Aug 04 2020