A336779 a(n) is the largest power of n such that all numbers n^k <= a(n), k=1,..,A336778(n)-1 can be exactly represented as double precision 64-bit floating point numbers according to the IEEE 754 standard. If a(n) is a power of 2, it is replaced by the corresponding negated exponent of 2.

-1023, 5559060566555523, -1022, 2384185791015625, 47751966659678405306351616, 1628413597910449, -1023, 1853020188851841, 10000000000000000000000, 4177248169415651, 410186270246002225336426103593500672, 3937376385699289, 426878854210636742656, 1946195068359375, -1020

Offset: 2

Author

Hugo Pfoertner, Aug 04 2020

Keywords

• sign
• fini
• look

Comments

The "power of 2" escape clause serves to avoid the corresponding numbers with more than 305 decimal digits in the DATA field.

Examples

			a(3) = 5559060566555523 = 3^33, because the next power 3^34 = 16677181699666569 cannot be exactly represented as a binary64 floating point number, but only rounded to 16677181699666568.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..1600

Crossrefs

Cf. A336774, A336775, A336776, A336778, A336780.

Formula

a(n) = n^(A336778(n)-1).