A250127 - OEIS

%I #15 Dec 23 2014 21:31:47

%S 1,5,7,11,13,103,177,206,684,1138,1368,1817,2046,2270,2485,4959,7411,

%T 19616,22061,24482,31776,220238,314155,345422,376714,532978,1592947,

%U 3707718,4235919,4763906,6874759,7929554,8984063,9511273

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

%e 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, ...

%e The corresponding list of pairs [n, A098550(n)/n] is:

%e [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], ...

%e It would be nice to know what curve these points lie on.

%o (Python)

%o from fractions import gcd

%o A250127_list, l1, l2, s, u, l, b = [1], 3, 2, 4, 1, 1, {}

%o for n in range(4,10**4):

%o ....i = s

%o ....while True:

%o ........if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:

%o ............l2, l1, b[i] = l1, i, 1

%o ............while s in b:

%o ................b.pop(s)

%o ................s += 1

%o ............if u*n < i*l:

%o ................A250127_list.append(n)

%o ................u, l = i, n

%o ............break

%o ........i += 1 # _Chai Wah Wu_, Dec 06 2014

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

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Dec 02 2014

%E a(23)-a(26) and extended example section by _Chai Wah Wu_, Dec 06 2014

%E a(27)-a(34) from _David Applegate_, Dec 18 2014