A250127 Numbers n where A098550(n)/n reaches a new high-water mark.

1, 5, 7, 11, 13, 103, 177, 206, 684, 1138, 1368, 1817, 2046, 2270, 2485, 4959, 7411, 19616, 22061, 24482, 31776, 220238, 314155, 345422, 376714, 532978, 1592947, 3707718, 4235919, 4763906, 6874759, 7929554, 8984063, 9511273

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Example

The record values of A098550(n)/n at these points are 1, 9/5, 15/7, 25/11, 35/13, 329/103, 581/177, 679/206, 3443/684, 5753/1138, 6941/1368, 9229/1817, 947/186, 11561/2270, 14963/2485, 30043/4959, 45071/7411, 120107/19616, 10399/1697, 150137/24482, 255221/31776, 1786819/220238, 2552567/314155, 2807737/345422, 3063077/376714, 4849921/532978, ...
The corresponding list of pairs [n, A098550(n)/n] is:
[1, 1.], [5, 1.800000000], [7, 2.142857143], [11, 2.272727273], [13, 2.692307692], [103, 3.194174757], [177, 3.282485876], [206, 3.296116505], [684, 5.033625731], [1138, 5.055360281], [1368, 5.073830409], [1817, 5.079251513], [2046, 5.091397849], [2270, 5.092951542], [2485, 6.021327968], [4959, 6.058277879], [7411, 6.081635407], [19616, 6.122909869], [22061, 6.127872717], [24482, 6.132546361], [31776, 8.031879406], [220238, 8.113127616], [314155, 8.125183428], [345422, 8.128425520], [376714, 8.131041055], [532978, 9.099664526], ...
It would be nice to know what curve these points lie on.

Prog

(Python)
from fractions import gcd
A250127_list, l1, l2, s, u, l, b = [1], 3, 2, 4, 1, 1, {}
for n in range(4, 10**4):
....i = s
....while True:
........if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
............l2, l1, b[i] = l1, i, 1
............while s in b:
................b.pop(s)
................s += 1
............if u*n < i*l:
................A250127_list.append(n)
................u, l = i, n
............break
........i += 1 # Chai Wah Wu, Dec 06 2014

Crossrefs

Cf. A098550. See A251415 for the values of A098550 at these points.

Sequence in context: A339953 A220951 A136055 * A181494 A125293 A354164

Adjacent sequences: A250124 A250125 A250126 * A250128 A250129 A250130

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 02 2014

Extensions

a(23)-a(26) and extended example section by Chai Wah Wu, Dec 06 2014

a(27)-a(34) from David Applegate, Dec 18 2014

Status

approved