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%I A056825 #20 Sep 13 2021 21:00:50
%S A056825 2,3,6,7,11,13,14,18,19,21,22,23,27,28,29,31,34,38,41,43,44,45,46,47,
%T A056825 51,52,53,54,55,57,58,59,61,62,66,67,69,70,71,73,76,77,79,83,85,86,88,
%U A056825 89,91,92,93,94,97,98,102,103,106,107,108,109,111,113,114,115,116,117,118,119
%N 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.
%D A056825 O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954. (Sec. 26)
%H A056825 Chai Wah Wu, <a href="/A056825/b056825.txt">Table of n, a(n) for n = 1..10000</a>
%H A056825 Len Smiley, <a href="http://www.math.uaa.alaska.edu/~smiley/cfpalin2.html">Initial Euler - Muir Polynomials</a>
%e A056825 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.
%o A056825 (Python)
%o A056825 from sympy.ntheory.continued_fraction import continued_fraction_periodic
%o A056825 A056825_list, nset, n = [], set(), 1
%o A056825 while len(A056825_list) < 10000:
%o A056825     cf = continued_fraction_periodic(0,1,n)
%o A056825     if len(cf) > 1:
%o A056825         pal = tuple(cf[1][:-1])
%o A056825         if pal not in nset:
%o A056825             A056825_list.append(n)
%o A056825             nset.add(pal)
%o A056825     n += 1 # _Chai Wah Wu_, Sep 13 2021
%K A056825 nonn
%O A056825 1,1
%A A056825 _Len Smiley_, Aug 29 2000
%E A056825 More terms from _Naohiro Nomoto_, Nov 09 2001
%E A056825 Missing terms 108 and 117 added by _Chai Wah Wu_, Sep 13 2021

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