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 A146326 Length of the period of the continued fraction of (1+sqrt(n))/2. 40
 0, 2, 2, 0, 1, 4, 4, 4, 0, 2, 2, 2, 1, 4, 2, 0, 3, 6, 6, 4, 2, 6, 4, 4, 0, 2, 2, 4, 1, 2, 8, 4, 4, 4, 2, 0, 3, 6, 6, 8, 5, 4, 10, 6, 2, 8, 4, 4, 0, 2, 2, 4, 1, 6, 4, 2, 6, 6, 6, 4, 3, 4, 2, 0, 3, 6, 10, 6, 4, 6, 8, 4, 9, 6, 4, 8, 2, 4, 4, 4, 0, 2, 2, 2, 1, 6, 2, 8, 7, 2, 8, 8, 2, 12, 4, 8, 9, 4, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First occurrence of n in this sequence see A146343. Records see A146344. Indices where records occurred see A146345. a(n) =0 for n = k^2 (A000290). a(n) =1 for n = 4 k^2 + 4 k + 5 (A078370). For primes see A005473. a(n) =2 for n in A146327. For primes see A056899. a(n) =3 for n in A146328. For primes see A146348. a(n) =4 for n in A146329. For primes see A028871 - {2}. a(n) =5 for n in A146330. For primes see A146350. a(n) =6 for n in A146331. For primes see A146351. a(n) =7 for n in A146332. For primes see A146352. a(n) =8 for n in A146333. For primes see A146353. a(n) =9 for n in A143577. For primes see A146354. a(n)=10 for n in A146334. For primes see A146355. a(n)=11 for n in A146335. For primes see A146356. a(n)=12 for n in A146336. For primes see A146357. a(n)=13 for n in A333640. For primes see A146358. a(n)=14 for n in A146337. For primes see A146359. a(n)=15 for n in A146338. For primes see A146360. a(n)=16 for n in A146339. For primes see A146361. a(n)=17 for n in A146340. For primes see A146362. LINKS R. J. Mathar, Table of n, a(n) for n = 1..20000. FORMULA a(n) = 0 iff n is a square (A000290). - Robert G. Wilson v, Apr 11 2017 EXAMPLE a(2) = 2 because continued fraction of (1+sqrt(2))/2 = 1, 4, 1, 4, 1, 4, 1, ... has period (1,4) length 2. MAPLE A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%) ; else 0 ; fi; end: seq(A146326(n), n=1..100) ; # R. J. Mathar, Sep 06 2009 MATHEMATICA Table[cf = ContinuedFraction[(1 + Sqrt[n])/2]; If[Head[cf[[-1]]] === List, Length[cf[[-1]]], 0], {n, 100}] f[n_] := Length@ ContinuedFraction[(1 + Sqrt[n])/2][[-1]]; Array[f, 100] (* Robert G. Wilson v, Apr 11 2017 *) CROSSREFS Cf. A003285, A146343, A146344, A146345. Cf. also A000290, A078370, A146327-A146342; A005473, A056899, A146348-A146362. Sequence in context: A214776 A317575 A295653 * A276727 A267617 A158852 Adjacent sequences:  A146323 A146324 A146325 * A146327 A146328 A146329 KEYWORD nonn AUTHOR Artur Jasinski, Oct 30 2008 EXTENSIONS a(39) and a(68) corrected by R. J. Mathar, Sep 06 2009 STATUS approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)