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.

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, 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, 5, 22, 4, 5, 4, 6, 4, 5, 4, 8, 4, 5, 4, 6, 4, 5, 4, 11, 4, 5, 4

Offset

2,1

Comments

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..16384

Hugo Pfoertner, Comparison with exact results, range n=2..128, computed on x86-64 architecture.

Edmund Weitz, IEEE 754 Calculator, uses JavaScript (2016).

Wikipedia, IEEE 754.

Crossrefs

Cf. A336775, A336778, A336779.

Sequence in context: A351247 A303324 A121374 * A252487 A160638 A188829

Adjacent sequences: A336771 A336772 A336773 * A336775 A336776 A336777

Keyword

nonn,fini

Author

Hugo Pfoertner, Aug 04 2020

Status

approved