login
Values of k at which the ratio k/A005132(k) sets a new record.
2

%I #16 Jan 09 2020 19:38:56

%S 1,4,31,62,64,111,129,131,30764,30766,30768,56127,56167,56199,56513,

%T 56515,56827,99734,58055311,904012796,904032692,1610175617,1610178287,

%U 1610186343,2789149734,13808214835,325374625053,325374625245

%N Values of k at which the ratio k/A005132(k) sets a new record.

%C No other terms < 4.61 * 10^11.

%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>

%e A005132(131) = 4, 131/4 = 32.75, a higher ratio than any smaller term in A005132, so 131 is in the sequence.

%t Block[{s = MapIndexed[First[#2]/#1 &, Rest@ Nest[Append[#, If[And[#3 > 0, FreeQ[#1, #3]], #3, #1[[-1]] + #2]] & @@ {#, Length@ #, #[[-1]] - Length@ #} &, {0}, 10^5]], t}, t = Union@ FoldList[Max, Rest@ s]; MapAt[# - 1 &, #, 1] &@ Map[FirstPosition[s, #][[1]] &, t]] (* _Michael De Vlieger_, Jan 01 2020 *)

%Y Cf. A005132, A064622, A330789.

%K nonn

%O 1,2

%A _Jud McCranie_, Dec 31 2019