A059800 Smallest prime p such that the quotient-cycle length in continued fraction expansion of sqrt(p) is n: smallest prime p(m) for which A054269(m)=n.

2, 3, 41, 7, 13, 19, 73, 31, 113, 43, 61, 103, 193, 179, 109, 191, 157, 139, 337, 151, 181, 491, 853, 271, 457, 211, 1109, 487, 821, 379, 601, 463, 613, 331, 1061, 1439, 421, 619, 541, 1399, 1117, 571, 1153, 823, 1249, 739, 1069, 631, 1021, 1051, 1201

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..2000

Formula

a(n) = Min{p|A054269(sequence number of p)=n; p is prime}.

Example

The quotient-cycle length L=9=A054269(m) first appears for p(30)=113, so a(9)=113 namely, at first A054269(30)=9; a(A054269(30)) = p(30) = 113 = a(9). The quotient cycle with L=16 first emerges for sqrt(191) and it is: cfrac(sqrt(191), 'periodic', 'quotients')= [[13],[1,4,1,1,3,2,2,13,2 2,3,1,1,4,1,26]].

Crossrefs

Cf. A054269.

Cf. A013646, A130272

Sequence in context: A288519 A240588 A013646 * A330293 A302687 A280893

Adjacent sequences: A059797 A059798 A059799 * A059801 A059802 A059803

Keyword

nonn

Author

Labos Elemer, Feb 23 2001

Status

approved