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, 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)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Len Smiley, Initial Euler - Muir Polynomials

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 * A070757 A056956 A171033

Adjacent sequences: A056822 A056823 A056824 * A056826 A056827 A056828

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