A336778 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 64-bit double precision floats according to the IEEE 754 standard.

1024, 34, 512, 23, 34, 19, 342, 17, 23, 16, 34, 15, 19, 14, 256, 13, 17, 13, 23, 13, 16, 12, 34, 12, 15, 12, 19, 11, 14, 11, 205, 11, 13, 11, 17, 11, 13, 11, 23, 10, 13, 10, 16, 10, 12, 10, 34, 10, 12, 10, 15, 10, 12, 10, 19, 10, 11, 10, 14, 9, 11, 9, 171, 9, 11

Offset: 2

Author

Hugo Pfoertner, Aug 04 2020

Keywords

• nonn
• fini

Comments

See A336774 for more information and links.

For n a power of two the first deviation is caused by exceeding the maximum representable number of the binary64 double precision floating point format with result +infinity in standard conforming implementations.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..1600
• Hugo Pfoertner, Comparison with exact results, range n=2..128, computed on x86-64 architecture.

Crossrefs

Cf. A336774, A336775, A336776, A336779, A336780.