

A013946


Least d for which the number with continued fraction [n,n,n,n...] is in Q(sqrt(d)).


6



5, 2, 13, 5, 29, 10, 53, 17, 85, 26, 5, 37, 173, 2, 229, 65, 293, 82, 365, 101, 445, 122, 533, 145, 629, 170, 733, 197, 5, 226, 965, 257, 1093, 290, 1229, 13, 1373, 362, 61, 401, 1685, 442, 1853, 485, 2029, 530, 2213, 577, 2405, 626, 2605, 677, 2813, 730, 3029, 785, 3253
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000
Robin James Spivey, Close encounters of the golden and silver ratios, Notes on Number Theory and Discrete Mathematics (2019) Vol. 25, No. 3, 170184.


FORMULA

a(n) = A007913(n^2+4).  David W. Wilson, Dec 08 2010


MATHEMATICA

z = 5000; u = Table[{p, e} = Transpose[FactorInteger[n]];
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 *)


PROG

(PARI) A013946(n)=core(n^2+4) \\ M. F. Hasler, Dec 08 2010


CROSSREFS

a(n) = 2 is equivalent to "n is in the sequence A077444", a(n) = 5 is equivalent to "n is in the sequence A002878".
Sequence in context: A082153 A283944 A294684 * A261327 A330613 A085436
Adjacent sequences: A013943 A013944 A013945 * A013947 A013948 A013949


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

More terms from David W. Wilson


STATUS

approved



