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A233587 Coefficients of the generalized continued fraction expansion sqrt(7) = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).

%I A233587 #20 Mar 25 2025 15:02:30
%S A233587 2,3,30,34,111,235,3775,5052,7352,9091,34991,35530,53424,57290,66023,
%T A233587 1409179,1519111,1725990,1812396,4370835,4507156,4655396,44257080,
%U A233587 234755198,261519946,264374278,273487975
%N A233587 Coefficients of the generalized continued fraction expansion sqrt(7) = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).
%C A233587 For more details on Blazys' expansions, see A233582.
%C A233587 Sqrt(7) is the first square root of a natural number with an a-periodic Blazys' expansion (see A233592 and A233593).
%H A233587 Stanislav Sykora, <a href="/A233587/b233587.txt">Table of n, a(n) for n = 1..1000</a>
%F A233587 sqrt(7) = 2+2/(3+3/(30+30/(34+34/(111+...)))).
%t A233587 BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[Sqrt@7, 32] (* _Robert G. Wilson v_, May 22 2014 *)
%o A233587 (PARI) bx(x, nmax)={local(c, v, k); \\ Blazys expansion function
%o A233587 v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }
%o A233587 bx(sqrt(7), 1000) \\ Execution; use very high real precision
%Y A233587 Cf. Blazys' expansions: A233582 (Pi), A233583 (e), A233584 (sqrt(e)), A233585 (1/gamma), A233585 (2*gamma) and Blazys' continued fractions: A233588, A233589, A233590, A233591.
%Y A233587 Cf. A010465, A010121.
%K A233587 nonn
%O A233587 1,1
%A A233587 _Stanislav Sykora_, Jan 06 2014