login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
8

%I #14 Aug 06 2020 03:57:05

%S 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 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 5,22,4,5,4,6,4,5,4,8,4,5,4,6,4,5,4,11,4,5,4

%N 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 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 Hugo Pfoertner, <a href="/A336774/b336774.txt">Table of n, a(n) for n = 2..16384</a>

%H Hugo Pfoertner, <a href="/A336774/a336774.txt">Comparison with exact results</a>, range n=2..128, computed on x86-64 architecture.

%H Edmund Weitz, <a href="http://weitz.de/ieee/">IEEE 754 Calculator</a>, uses JavaScript (2016).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/IEEE_754">IEEE 754</a>.

%Y Cf. A336775, A336778, A336779.

%K nonn,fini

%O 2,1

%A _Hugo Pfoertner_, Aug 04 2020