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

2,1

Comments

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

Links

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

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A069437 A212934 A263168 * A030001 A176764 A351262

Adjacent sequences: A336776 A336777 A336778 * A336780 A336781 A336782

Keyword

sign,fini,look

Author

Hugo Pfoertner, Aug 04 2020

Status

approved