This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A146348 Primes p such that continued fraction of (1+sqrt(p))/2 has period 3. 37
 17, 37, 61, 101, 197, 257, 317, 401, 461, 557, 577, 677, 773, 1129, 1297, 1429, 1601, 1877, 1901, 2917, 3137, 4357, 4597, 5417, 5477, 6053, 7057, 8101, 8761, 8837, 10733, 11621, 12101, 13457, 13877, 14401, 15277, 15377, 15877, 16333, 16901, 17737, 17957, 18329, 21317, 22501, 23593, 24337, 25601, 28901, 30137, 30977, 32401, 33857, 41453, 41617, 42437, 44101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes in A146328. Finite A050952 is subset of this sequence. From Michel Lagneau, Sep 03 2014: (Start) The primes of the form p = n^2+1 for n>2 are in the sequence, and the continued fraction of (1+sqrt(p))/2 is [n/2; 1, 1, n-1, 1, 1, n-1, 1, 1,...] with the period (1, 1, n-1). We observe that the other primes {61, 317, 461, 557, 773, 1129, 1429,…} are prime divisors of composites numbers of the form k^2+1 where k = 11, 114, 48, 118, 317, 168, 620,… . (End) Another possibly infinite subset of the sequence is primes of the form 100*k^2-44*k+5, where the continued fraction is [5*k-1; 2, 2, 10*k-3, ...] with period [2, 2, 10*k-3].  This includes {61, 317, 773, 1429, 4597, 6053, ...}. - Robert Israel, Sep 03 2014 LINKS Zak Seidov, Table of n, a(n) for n = 1..200 MAPLE A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146348 := proc(n) RETURN(isprime(n) and A146326(n) = 3) ; end: for n from 2 to 4000 do if isA146348(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Sep 06 2009 MATHEMATICA okQ[n_] := Length[ContinuedFraction[(1 + Sqrt[n])/2][[2]]] == 3; Select[Prime[Range[100]], okQ] CROSSREFS Cf. A000290, A050952, A078370, A146326-A146345, A146348-A146360, A146363. Sequence in context: A146328 A161549 A269788 * A050952 A256517 A323603 Adjacent sequences:  A146345 A146346 A146347 * A146349 A146350 A146351 KEYWORD nonn AUTHOR Artur Jasinski, Oct 30 2008 EXTENSIONS 1019 removed; more terms added by R. J. Mathar, Sep 06 2009 More terms from Zak Seidov, Mar 09 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 18 07:10 EDT 2019. Contains 325134 sequences. (Running on oeis4.)