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A374856
a(n) is the least integer m such that the distance of x_m from its nearest integer is less than 1/n, where x_m is the m-th root of digamma(x+1).
1
0, 1, 6, 23, 76, 231, 681, 1968, 5605, 15817, 44324, 123573, 343157, 950000
OFFSET
1,3
COMMENTS
a(n) approximately equals exp(Pi/tan(Pi/n)).
EXAMPLE
0 - -0.461632144968362 < 1/1
2 - 1.50408300826446 < 1/2
7 - 6.66716244155689 < 1/3
24 - 23.7502429843061 < 1/4
77 - 76.8003723367285 < 1/5
232 - 231.833395691244 < 1/6
PROG
(Python)
from mpmath import findroot, digamma, mp
i, seq, n = 1, [], 101
for j in range(n):
root = findroot(lambda x: digamma(x+1), (-j-1+1e-10, -j-0.5), solver='anderson')
if root - mp.nint(root) < 1/i:
seq.append(j)
i += 1
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jwalin Bhatt, Sep 16 2024
STATUS
approved