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

Author

Hugo Pfoertner, Aug 04 2020

Keywords

• nonn
• fini

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.