login
A056825
Numbers such that no smaller positive integer has the same maximal palindrome in the periodic part of the simple continued fraction for its square root.
2
2, 3, 6, 7, 11, 13, 14, 18, 19, 21, 22, 23, 27, 28, 29, 31, 34, 38, 41, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 66, 67, 69, 70, 71, 73, 76, 77, 79, 83, 85, 86, 88, 89, 91, 92, 93, 94, 97, 98, 102, 103, 106, 107, 108, 109, 111, 113, 114, 115, 116, 117, 118, 119
OFFSET
1,1
REFERENCES
O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954. (Sec. 26)
EXAMPLE
33, 60 and 95 are not in the list because their square roots' simple continued fractions, [5,1,2,1,10,1,2,1,10,...], [7,1,2,1,14,...] and [9,1,2,1,18,...], have the same maximal palindrome in their periods as the square root of 14, [3,1,2,1,6,1,2,1,6,...] does.
PROG
(Python)
from sympy.ntheory.continued_fraction import continued_fraction_periodic
A056825_list, nset, n = [], set(), 1
while len(A056825_list) < 10000:
cf = continued_fraction_periodic(0, 1, n)
if len(cf) > 1:
pal = tuple(cf[1][:-1])
if pal not in nset:
A056825_list.append(n)
nset.add(pal)
n += 1 # Chai Wah Wu, Sep 13 2021
CROSSREFS
Sequence in context: A274546 A366641 A113545 * A372062 A070757 A056956
KEYWORD
nonn
AUTHOR
Len Smiley, Aug 29 2000
EXTENSIONS
More terms from Naohiro Nomoto, Nov 09 2001
Missing terms 108 and 117 added by Chai Wah Wu, Sep 13 2021
STATUS
approved