Irregular triangular array: every periodic simple continued fraction CF represents a quadratic irrational (c + f*sqrt(d))/b, where b,c,f,d are integers and d is squarefree. Row n of this array shows the distinct values of d as CF ranges through the periodic continued fractions having period an n-tuple of 1s and 3s.

A246922

Irregular triangular array: every periodic simple continued fraction CF represents a quadratic irrational (c + f*sqrt(d))/b, where b,c,f,d are integers and d is squarefree. Row n of this array shows the distinct values of d as CF ranges through the periodic continued fractions having period an n-tuple of 1s and 3s.

Terms

    a(0) =5a(1) =13a(2) =5a(3) =13a(4) =21a(5) =5a(6) =13a(7) =17a(8) =65a(9) =5a(10) =13a(11) =21a(12) =29a(13) =165a(14) =2805a(15) =5a(16) =13a(17) =61a(18) =317a(19) =445a(20) =1853a(21) =5933a(22) =30629a(23) =2a(24) =5a(25) =7a(26) =13a(27) =15a(28) =17a(29) =21

External references