A376207 Numbers k such that ceiling(2*Pi*k/sqrt(2)) != ceiling(Pi/arcsin(sqrt(2)/(2*k))).

1, 70, 569, 58704, 15770314

Offset: 1

Author

Hugo Pfoertner, Sep 15 2024

Keywords

• nonn
• more

Comments

2*n/sqrt(2) > 1/arcsin(sqrt(2)/(2*n)) for all n > 0.

Limit_{x->oo} 2*x/sqrt(2) - 1/arcsin(sqrt(2)/(2*x)) = 0.

Examples

			  n    k=a(n)        2*Pi*k/sqrt(2)   Pi/arcsin(sqrt(2)/(2*k))
  1         1         4.44288293816             4.000000000000
  2        70       311.00180567109           310.996516371805
  3       569      2528.00039181211          2527.999741125982
  4     58704    260815.00000164873        260814.999995341832
  5  15770314  70065659.00000001744      70065658.999999993965
		

Crossrefs

Cf. A063448, A376066.

Cf. A120702.