A334264 Numbers k > 1 such that (3/2)^k sets a new record for closest fractional part to 1/2.

2, 3, 5, 9, 11, 69, 420, 2361, 12432, 21565, 28226, 128389, 274555, 497269, 836000, 1151341, 1973112, 2202332, 2458844, 5402520

Offset: 1

Author

Ben Paul Thurston, Apr 20 2020

Keywords

• nonn
• more

Crossrefs

A081464 is also related to (3/2) to a power being a record distance from a value of an integer.

Cf. A002379, A034082, A179523.

Programs

Maple

off := 1; for i from 2 to 1000 do t := (1+1/2)^i-floor((1+1/2)^i); d := abs(1/2-t); if d < off then off := d; print(i) end if end do

Mathematica

dm = 1; r = 3/2; s = {}; Do[r *= 3/2; If[(d = Abs[r - Floor[r] - 1/2]) < dm, dm = d; AppendTo[s, n + 1]], {n, 1, 10^7}]; s (* Amiram Eldar, Jun 08 2020 *)

Extensions

a(8)-a(13) from Amiram Eldar, Jun 08 2020

a(14)-a(16) from Chai Wah Wu, Jul 02 2020

a(17)-a(20) from Bert Dobbelaere, Apr 25 2021