A251415 Values of A098550 where A098550(n)/n reaches a new high-water mark.

1, 9, 15, 25, 35, 329, 581, 679, 3443, 5753, 6941, 9229, 10417, 11561, 14963, 30043, 45071, 120107, 135187, 150137, 255221, 1786819, 2552567, 2807737, 3063077, 4849921, 14549573, 33948953, 38798741, 43648643, 63048061, 72747599, 82447327, 87297191

Offset

1,2

Comments

The prime factorizations of these numbers are 1, 3^2, 3*5, 5^2, 5*7, 7*47, 7*83, 7*97, 11*313, 11*523, 11*631, 11*839, 11*947, 11*1051, 13*1151, 13*2311, 13*3467, 13*9239, 13*10399, 13*11549, 17*15013, 17*105107, ... It would be nice to know what this is trying to tell us!

Links

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

Prog

(Python)
from fractions import gcd
A251415_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:
................A251415_list.append(i)
................u, l = i, n
............break
........i += 1 # Chai Wah Wu, Dec 06 2014

Crossrefs

Cf. A098550, A250127, A241416.

Sequence in context: A319529 A249730 A342418 * A109888 A193227 A014003

Adjacent sequences: A251412 A251413 A251414 * A251416 A251417 A251418

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 02 2014

Extensions

a(23)-a(26) added and typo in definition corrected by Chai Wah Wu, Dec 06 2014

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

Status

approved