The On-Line Encyclopedia of Integer Sequences (OEIS)

A146340 revision #19

A146340

Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 17.

521, 617, 709, 1433, 1597, 2549, 2909, 2965, 3161, 3581, 3821, 4013, 4285, 4649, 5501, 5585, 5693, 5813, 6197, 6409, 7825, 7853, 8093, 8125, 8573, 8917, 9281, 9665, 9677, 9925, 10265, 10597, 10973, 11273, 12085, 12805, 13061, 13109, 13613, 13957, 14677

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OFFSET

1,1

COMMENTS

For primes in this sequence see A146362.

LINKS

Table of n, a(n) for n=1..41.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..150 from Harvey P. Dale)

EXAMPLE

a(1) = 521 because continued fraction of (1+sqrt(521))/2 = 11, 1, 10, 2, 5, 4, 2, 1, 1, 1, 1, 2, 4, 5, 2, 10, 1, 21, 1, 10, 2, 5, 4, 2, 1, 1, 1, 1, 2, 4, 5, 2, 10, 1, 21, 1, 10, 2, 5, ... has period (1, 10, 2, 5, 4, 2, 1, 1, 1, 1, 2, 4, 5, 2, 10, 1, 21) length 17.

MAPLE

A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146340 := proc(n) RETURN(A146326(n) = 17) ; end: for n from 2 do if isA146340(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Sep 06 2009

MATHEMATICA

cf17Q[n_]:=Module[{s=(1+Sqrt[n])/2}, If[IntegerQ[s], 1, Length[ ContinuedFraction[ s][[2]]]]==17]; Select[Range[5000], cf17Q] (* Harvey P. Dale, Dec 20 2017 *)

CROSSREFS

Cf. A000290, A078370, A146326-A146345, A146348-A146360.

Sequence in context: A291998 A300395 A139663 * A146362 A050966 A113158

Adjacent sequences: A146337 A146338 A146339 * A146341 A146342 A146343

KEYWORD

more,nonn

AUTHOR

Artur Jasinski, Oct 30 2008

EXTENSIONS

998 and 1006 removed, sequence extended by R. J. Mathar, Sep 06 2009

More terms from Harvey P. Dale, Dec 20 2017

STATUS

approved