A351139 a(n) is the least k such that the continued fraction for sqrt(k) has periodic part [r, 1, 2, ..., n-1, n, n-1, ..., 1, 2r] for some positive integer r.

3, 14, 216, 25185, 23287359, 1953082923, 81112983931776, 6667182474680388, 699567746120736710880, 855784807474766398870755, 51592564054278677032777194015, 1474855822717073602911008555048040, 23175672095781915301598668218548941215, 474577479777785868138090462593743556930231

Offset: 1

Author

Giorgos Kalogeropoulos, Feb 02 2022

Keywords

• nonn

Examples

			a(3) = 216 because the continued fraction of sqrt(216) has periodic part [14; 1, 2, 3, 2, 1, 28] and this is the least number with this property.
		

Crossrefs

Cf. A013646.

Programs

Python

from itertools import count
from sympy.ntheory.continued_fraction import continued_fraction_reduce
def A351139(n):
    if n == 2:
        return 14
    for r in count(1):
        if (k := continued_fraction_reduce([r,list(range(1,n+1))+list(range(n-1,0,-1))+[2*r]])**2).is_integer:
            return k # Chai Wah Wu, Feb 09 2022