id:A091015 - OEIS Search Results

Search: id:A091015

Displaying 1-1 of 1 results found.

page 1

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

+0
1

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 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`For r=sqrt(n), the solutions to x^2=ceiling(xrfloor(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)= 2A002350(n)b(k-1)-b(k-2).`
	PROGRAM	`(PARI) a(n)=if(n<2, 1, x=1; while(abs(x^2-ceil(sqrt(n)xfloor(x/ sqrt(n))))>0, x++); x)`
	CROSSREFS	`Sequence in context: A141456 A137445 A011319 this_sequence A058147 A119954 A100804` `Adjacent sequences: A091012 A091013 A091014 this_sequence A091016 A091017 A091018`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004`

page 1

Search completed in 0.002 seconds

Last modified December 3 16:57 EST 2008. Contains 151279 sequences.

AT&T Labs Research