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A206578 The least number with exactly n ones in the continued fraction of its square root. 6
2, 3, 14, 7, 13, 91, 43, 115, 94, 819, 133, 1075, 211, 1219, 309, 871, 421, 1147, 244, 3427, 478, 2575, 991, 8791, 604, 3799, 886, 5539, 1381, 8851, 1279, 7303, 1561, 19519, 1759, 10339, 1831, 12871, 2038, 13771, 1999, 8611, 1516, 15871, 2731, 20875, 1726 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

It appears that only the odd-numbered terms 3 and 7 are prime; all other primes occur at even-numbered terms 0, 4, 6, 12, 16, 22, 28, 30, 34, ... In terms 0 to 1000, there are 268 primes and 632 semiprimes.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

MATHEMATICA

nn = 50; zeros = nn; t = Table[0, {nn}]; k = 2; While[zeros > 0, If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][[2]], 1]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = k; zeros--]]; k++]; Join[{2}, t]

PROG

(Python)

from sympy import continued_fraction_periodic

def A206578(n):

    m = 1

    while True:

        s = continued_fraction_periodic(0, 1, m)[-1]

        if isinstance(s, list) and s.count(1) == n:

            return m

        m += 1 # Chai Wah Wu, Jun 12 2017

CROSSREFS

Cf. A013647-A013650 (0-3), A020440-A020446 (4-10), A031779-A031868 (11-100).

Cf. A206582 (n twos), A206583 (n threes), A206584 (n fours), A206585 (n fives).

Sequence in context: A287858 A288648 A287912 * A056435 A244295 A032806

Adjacent sequences:  A206575 A206576 A206577 * A206579 A206580 A206581

KEYWORD

nonn

AUTHOR

T. D. Noe, Feb 24 2012

STATUS

approved

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Last modified January 16 14:39 EST 2022. Contains 350376 sequences. (Running on oeis4.)