A080680 Integer part of the square root of the n-th prime of the form 4k+1.

2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29

Offset: 1

Author

Reinhard Zumkeller, Mar 02 2003

Keywords

• nonn

Comments

a(n)^2 < A002330(n+2)^2 + A002331(n+2)^2 < a(n+1)^2.

Programs

Mathematica

Floor[Sqrt[#]]&/@Select[Prime[Range[300]],Mod[#,4]==1&] (* Harvey P. Dale, Jun 04 2023 *)

Formula

a(n) = A000196(A002144(n)).