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%I #16 Jun 15 2022 01:49:40
%S 1,2,3,1,2,3,5,3,1,2,3,3,6,5,3,1,2,3,7,3,7,7,5,3,1,2,3,5,6,3,9,5,5,5,
%T 3,1,2,3,3,3,4,3,11,9,7,13,5,3,1,2,3,7,6,7,5,3,7,8,7,5,12,5,3,1,2,3,
%U 11,3,9,7,9,3,8,6,5,13,7,5,5,3,1,2,3,3,6,11,3,7,6,3,9,9,11,17,5,5,12,5
%N Number of terms in continued fraction for sqrt(n), excl. 2nd and higher periods.
%D H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th edition, 1999, table 1.
%F a(n) = A003285(n) + 1. - _Andrey Zabolotskiy_, Jun 23 2020
%e a(2)=2: [1,(2)+ ]; a(3)=3: [1,(1,2)+ ]; a(4)=1: [2]; a(5)=2: [2,(4)+ ].
%o (Python)
%o from sympy import continued_fraction_periodic
%o def A067280(n): return len((a := continued_fraction_periodic(0,1,n))[:1]+(a[1] if a[1:] else [])) # _Chai Wah Wu_, Jun 14 2022
%Y Related sequences: 2 : A040000, ..., 44: A040037, 48: A040041, ..., 51: A040043, 56: A040048, 60: A040052, 63: A040055, ..., 66: A040057. 68: A040059, 72: A040063, 80: A040071.
%Y Related sequences: 45: A010135, ..., 47: A010137, 52: A010138, ..., 55: A010141, 57: A010142, ..., 59: A010144. 61: A010145, 62: A010146. 67: A010147, 69: A010148, ..., 71: A010150.
%Y Cf. A003285.
%K nonn,easy
%O 1,2
%A _Frank Ellermann_, Feb 23 2002
%E Name clarified by _Michel Marcus_, Jun 22 2020
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