A237611 Squarefree numbers of form 16*k^4 + 40*k^3 + 33*k^2 + 12*k + 2, k>0.

103, 734, 2711, 7234, 15887, 30638, 53839, 88226, 136919, 203422, 291623, 405794, 550591, 731054, 952607, 1221058, 1542599, 1923806, 2371639, 2893442, 3496943, 4190254, 4981871, 5880674, 6895927, 8037278, 10738786, 12320159, 14070062, 16000063, 18122114

Offset

1,1

Comments

The period of the continued fraction expansion of sqrt(a(n)) = A003285(a(n)) is 12, so the a(n) are a subset of A020351.

Links

Table of n, a(n) for n=1..31.

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

Mathematica

Select[Table[16k^4+40k^3+33k^2+12k+2, {k, 50}], SquareFreeQ] (* Harvey P. Dale, May 16 2014 *)

Prog

(PARI) list(n)=for(n=1, 50, t=16*n^4 + 40*n^3 + 33*n^2 + 12*n + 2; if(issquarefree(t), print1(t, ", ")))

Crossrefs

Sequence in context: A082883 A191357 A264824 * A077405 A262758 A023355

Adjacent sequences: A237608 A237609 A237610 * A237612 A237613 A237614

Keyword

nonn

Author

Ralf Stephan, Feb 10 2014

Extensions

Definition corrected by Harvey P. Dale, May 16 2014

Status

approved