A251415 Values of A098550 where A098550(k)/k reaches a record high.

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, 111546389

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..35.

Prog

(Python)
from math 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, A241416, A250127.

Sequence in context: A319529 A249730 A342418 * A109888 A193227 A014003

Adjacent sequences: A251412 A251413 A251414 * A251416 A251417 A251418

Keyword

nonn

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

a(35) from Jinyuan Wang, Jan 26 2025

Status

approved