A178805 Numbers k such that ||k/log(k)|| reaches a new minimum, where ||x|| is the distance from x to the nearest integer.

2, 5, 9, 13, 17, 163, 53453, 110673, 715533, 1432276, 6517719, 11523158, 11985596, 24102781, 254977309, 451207448, 1219588338, 2048539023, 10066616717, 42116139191, 47657002570, 73831354169, 122478947521, 143949453227, 3040705645816, 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 Kevin O'Bryant in a Math OverFlow comment. Closely related to A178806.

Added 15 more terms from Noam D. Elkies (second MathOverflow link). - T. D. Noe, Feb 12 2013

Links

• MathOverflow, Why Is 163/ln(163) a Near-Integer?
• MathOverflow, When is n/ln(n) close to an integer?

Crossrefs

Cf. A050499 (nearest integer to n/log(n)), A178806.

Programs

Mathematica

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