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%I #25 Apr 25 2021 03:21:15
%S 2,3,5,9,11,69,420,2361,12432,21565,28226,128389,274555,497269,836000,
%T 1151341,1973112,2202332,2458844,5402520
%N Numbers k > 1 such that (3/2)^k sets a new record for closest fractional part to 1/2.
%p 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
%t 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 *)
%Y A081464 is also related to (3/2) to a power being a record distance from a value of an integer.
%Y Cf. A002379, A034082, A179523.
%K nonn,more
%O 1,1
%A _Ben Paul Thurston_, Apr 20 2020
%E a(8)-a(13) from _Amiram Eldar_, Jun 08 2020
%E a(14)-a(16) from _Chai Wah Wu_, Jul 02 2020
%E a(17)-a(20) from _Bert Dobbelaere_, Apr 25 2021