A040007 -id:A040007 - cp's OEIS frontend

A010468 Decimal expansion of square root of 11.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 3 followed by {3, 6} repeated. - Harry J. Smith, Jun 02 2009

			3.316624790355399849114932736670686683927088545589353597058682146116484...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Michael Penn, A famous trig equation, YouTube video, 2021.
Index entries for algebraic numbers, degree 2

Cf. A040007 (continued fraction).

RealDigits[N[Sqrt[11],200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

default(realprecision, 20080); x=sqrt(11); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010468.txt", n, " ", d));  \\ Harry J. Smith, Jun 02 2009

A307508 Primes p for which the continued fraction expansion of sqrt(p) does not have a 1 in the second position.

Original entry on oeis.org

2, 5, 11, 17, 19, 29, 37, 41, 53, 67, 71, 83, 89, 101, 103, 107, 109, 127, 131, 149, 151, 173, 179, 181, 197, 199, 227, 229, 233, 239, 257, 263, 269, 271, 293, 331, 337, 367, 373, 379, 401, 409, 419, 443, 449, 457, 461, 487, 491, 499, 503, 541, 547, 577, 587, 593, 599

Offset: 1

Michel Marcus, Apr 11 2019

nonn

These are the primes that are located between a square number and the following oblong number. - Charles Kusniec, Apr 17 2020

Primes in A063656. - Charles Kusniec, Sep 04 2022

			For p = 2,  we have [1; 2, ...]; see A040000.
For p = 5,  we have [2; 4, ...]; see A040002.
For p = 11, we have [3; 3, ...]; see A040007.

Michel Marcus, Table of n, a(n) for n = 1..5000
Piotr Miska and Maciej Ulas, On consecutive 1's in continued fractions expansions of square roots of prime numbers, Experimental Mathematics, 31:1 (2022), 238-251. Also arXiv:1904.03404 [math.NT], 2019.
Index entries for continued fractions for constants

Cf. A040000, A040002, A040007, A067614, A307453, A063656.

Complement of A334163 with respect to the primes.

isok(p) = isprime(p) && contfrac(sqrt(p))[2] != 1;

cp's OEIS Frontend

A010468 Decimal expansion of square root of 11.

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