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%I #30 Mar 25 2024 12:05:58
%S 5,2,13,5,29,10,53,17,85,26,5,37,173,2,229,65,293,82,365,101,445,122,
%T 533,145,629,170,733,197,5,226,965,257,1093,290,1229,13,1373,362,61,
%U 401,1685,442,1853,485,2029,530,2213,577,2405,626,2605,677,2813,730,3029,785,3253
%N Least d for which the number with continued fraction [n,n,n,n...] is in Q(sqrt(d)).
%C Square roots of a(n) are found in the limiting ratios of A000045, A001333, A003688, A015448, A015449, A015451 and so on. I.e., the limiting ratios are the golden ratio, silver mean, bronze ratio and so on. - _Mats Granvik_, Oct 20 2010
%H Clark Kimberling, <a href="/A013946/b013946.txt">Table of n, a(n) for n = 1..1000</a>
%H Robin James Spivey, <a href="https://doi.org/10.7546/nntdm.2019.25.3.170-184">Close encounters of the golden and silver ratios</a>, Notes on Number Theory and Discrete Mathematics (2019) Vol. 25, No. 3, 170-184.
%H Ofer Yifrach-Stav, <a href="https://hal.science/tel-04513104">Fast and Private Pool Testing and Contributions to Experimental Mathematics</a>, Doctoral thesis, École normale supérieure (Paris, France), HAL Science [math.cs] 2024, Art. No. tel-04513104. See p. 104.
%F a(n) = A007913(n^2+4). - _David W. Wilson_, Dec 08 2010
%t z = 5000; u = Table[{p, e} = Transpose[FactorInteger[n]];
%t Times @@ (p^Mod[e, 2]), {n, z}]; Table[u[[n^2 + 4]], {n, 1, Sqrt[z - 4]}] (* _Clark Kimberling_, Jul 20 2015, based on _T. D. Noe_'s program at A007913 *)
%o (PARI) A013946(n)=core(n^2+4) \\ _M. F. Hasler_, Dec 08 2010
%Y a(n) = 2 is equivalent to "n is in the sequence A077444", a(n) = 5 is equivalent to "n is in the sequence A002878".
%K nonn
%O 1,1
%A _Clark Kimberling_
%E More terms from _David W. Wilson_
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