A010542 - OEIS

%I #21 Feb 11 2025 14:47:20

%S 9,5,3,9,3,9,2,0,1,4,1,6,9,4,5,6,4,9,1,5,2,6,2,1,5,8,6,0,2,3,2,2,6,5,

%T 4,0,2,5,4,6,2,3,4,2,5,2,5,0,5,4,5,7,5,3,9,0,8,1,5,1,8,5,2,9,1,0,3,6,

%U 2,5,5,2,3,0,5,6,5,0,7,2,1,8,2,7,7,8,2,1,7,6,4,4,9,1,2,2,0,6,9

%N Decimal expansion of square root of 91.

%C Continued fraction expansion is 9 followed by {1, 1, 5, 1, 5, 1, 1, 18} repeated. - _Harry J. Smith_, Jun 11 2009

%H Harry J. Smith, <a href="/A010542/b010542.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%e 9.53939201416945649152621586023226540254623...

%t RealDigits[N[Sqrt[91],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 04 2012 *)

%o (PARI) { default(realprecision, 20080); x=sqrt(91); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010542.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 11 2009

%o (Python)

%o from math import isqrt

%o def aupton(nn): return list(map(int, str(isqrt(91 * 10**(2*nn)))))[:nn]

%o print(aupton(100)) # _Michael S. Branicky_, Sep 05 2021

%Y Cf. A010162 (continued fraction).

%K nonn,cons,changed

%O 1,1

%A _N. J. A. Sloane_