A091015 Least integer x>0 such that x^2=ceiling(x*r*floor(x/r)) where r=sqrt(n).

1, 3, 2, 2, 9, 5, 8, 3, 3, 19, 10, 7, 649, 15, 4, 4, 33, 17, 170, 9, 55, 197, 24, 5, 5, 51, 26, 127, 9801, 11, 1520, 17, 23, 35, 6, 6, 73, 37, 25, 19, 2049, 13, 3482, 199, 161, 24335, 48, 7, 7, 99, 50, 649, 66249, 485, 89, 15, 151, 19603, 530, 31

Offset

1,2

Comments

For r=sqrt(n), the solutions to x^2=ceiling(x*r*floor(x/r)) appear to be given by the Chebyshev polynomial T(k,x) k>0 evaluated at x=a(n). These solutions also seem to be given by a sequence (b(k))_(k>=0) satisfying the recurrence b(k)= 2*A002350(n)*b(k-1)-b(k-2).

Links

Table of n, a(n) for n=1..60.

Prog

(PARI) a(n)=if(n<2, 1, x=1; while(abs(x^2-ceil(sqrt(n)*x*floor(x/ sqrt(n))))>0, x++); x)

Crossrefs

Sequence in context: A176530 A011319 A177460 * A256097 A058147 A193344

Adjacent sequences: A091012 A091013 A091014 * A091016 A091017 A091018

Keyword

nonn

Author

Benoit Cloitre, Feb 14 2004

Status

approved