A031401 Period of continued fraction for sqrt(A031400(n)).
1, 2, 4, 8, 4, 4, 4, 4, 4, 4, 4
Offset: 1
Crossrefs
Cf. A031400.
Extensions
a(10)-a(11) from Chai Wah Wu, Jan 26 2021
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
11 is in the sequence because sqrt(11) = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + 1/...)))), period 2: [3, 6] and sqrt(12) = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + 1/...)))), period 2: [2, 6].
sqrt(prime(97)) = sqrt(509) has continued fraction [22; 1, 1, 3, 1, 1, 2, 10, 1, 8, 8, 1, 10, 2, 1, 1, 3, 1, 1, 44, ...], period 19. sqrt(prime(98)) = sqrt(521) has continued fraction [22; 1, 4, 1, 2, 1, 2, 8, 1, 3, 3, 1, 8, 2, 1, 2, 1, 4, 1, 44, ...], period 19. These are the first 2 consecutive primes with the same period of continued fraction for square root, so a(2) = 97.
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