A237604 Numbers of form D^2 + 4d, with D odd, d divides D, and 1 < d < D.

93, 237, 245, 453, 469, 645, 741, 765, 1101, 1133, 1245, 1253, 1533, 1573, 2037, 2045, 2061, 2085, 2429, 2613, 2669, 3045, 3069, 3261, 3325, 3981, 3997, 4005, 4053, 4245, 4277, 4773, 4853, 5637, 5645, 5685, 5725, 5957, 5973, 6573, 6597, 6669, 7245, 7293, 7581, 7685, 8309

Offset: 1

Author

Ralf Stephan, Feb 10 2014

Keywords

• nonn

Comments

The period of the continued fraction expansion of sqrt(a(n)) = A003285(a(n)) is 10, so the a(n) are a subset of A020349. The periodic part of the continued fraction of sqrt(a(n)) is (D-d)/(2d),1,1,(D-1)/2,2D/d,(D-1)/2,1,1,(D-d)/(2d),2D. See the Bernstein paper.

a(n) seems to be always congruent 5 (mod 8).

Links

• Leon Bernstein, Fundamental units and cycles in the period of real quadratic number fields, I. Pacific J. Math 63 (1976): 37-61.

Crossrefs

Cf. A003285, A020349.

Programs

PARI

list(n)=for(i=1,n,D=2*i+1;fordiv(D,d,if(d>1&&d