A178806 Numbers n such that ||n/log(n)|| * log(n) reaches a new minimum, where ||x|| is the distance from x to the nearest integer.

2, 17, 163, 715533, 1432276, 6517719, 11523158, 11985596, 24102781, 254977309, 451207448, 1219588338, 2048539023, 10066616717, 42116139191, 47657002570, 73831354169, 122478947521, 143949453227, 3152420311977, 5624690531099, 14964977749017, 25999244327633, 92799025313425, 164330745650026, 604329910739082

Offset: 1

Author

T. D. Noe, Jun 16 2010

Keywords

• nonn

Comments

The first 9 terms are from Will Jagy in a MathOverflow answer. Closely related to A178805.

Added 14 more terms from Noam D. Elkies (second MathOverflow link). - T. D. Noe, Feb 12 2013

Links

• MathOverflow, When is n/ln(n) close to an integer?
• MathOverflow, When is n/ln(n) close to an integer?

Crossrefs

Cf. A050499 (nearest integer to n/log(n)).

Programs

Mathematica

mn=Infinity; n=2; Table[While[r=N[n/Log[n]]; diff=Log[n] Abs[r-Round[r]]; diff>=mn, n++ ]; mn=diff; Print[{n,mn}]; n, {9}]