A064621
Values of A005132(n) at which the ratio A005132(n)/n sets a new record.
Original entry on oeis.org
1, 3, 6, 13, 20, 62, 113, 224, 367, 494, 833, 9169, 131313, 155719, 180118, 280766754, 3454917187, 31685027464, 152431947617, 629621648241
Offset: 1
A005132(7)=20, 20/7 = 2.857..., larger than the ratio for any smaller value of n.
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Block[{s = Nest[Append[#1, If[And[#3 > 0, FreeQ[#1, #3]], #3, #1[[-1]] + #2]] & @@ {#1, #2, #1[[-1]] - #2} & @@ {#, Length@ #} &, {0}, 200000], t}, t = MapIndexed[#1/First@ #2 &, s]; Rest@ Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]] ] (* Michael De Vlieger, Dec 29 2019 *)
A330788
Values of k at which the ratio k/A005132(k) sets a new record.
Original entry on oeis.org
1, 4, 31, 62, 64, 111, 129, 131, 30764, 30766, 30768, 56127, 56167, 56199, 56513, 56515, 56827, 99734, 58055311, 904012796, 904032692, 1610175617, 1610178287, 1610186343, 2789149734, 13808214835, 325374625053, 325374625245
Offset: 1
A005132(131) = 4, 131/4 = 32.75, a higher ratio than any smaller term in A005132, so 131 is in the sequence.
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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 *)
A330789
Terms of A005132 corresponding to the values in A330788.
Original entry on oeis.org
1, 2, 14, 27, 26, 40, 5, 4, 830, 829, 828, 1414, 1354, 1306, 835, 834, 366, 19, 4202, 57520, 14804, 23289, 14510, 2426, 2405, 1814, 1643, 1355
Offset: 1
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Block[{s = Rest@ Nest[Append[#, If[And[#3 > 0, FreeQ[#1, #3]], #3, #1[[-1]] + #2]] & @@ {#, Length@ #, #[[-1]] - Length@ #} &, {0}, 10^5], t, u}, t = MapIndexed[First[#2]/#1 &, s]; u = MapAt[1 &, #, 1] &@ Union@ FoldList[Max, Rest@ t]; Map[s[[ FirstPosition[t, #][[1]] ]] &, u]] (* Michael De Vlieger, Jan 01 2020 *)
Showing 1-3 of 3 results.
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