A106033 a(n) is the least number k such that n*prime(n)+k is a perfect square.

2, 3, 1, 8, 9, 3, 2, 17, 18, 34, 20, 40, 43, 23, 24, 52, 21, 58, 23, 24, 67, 26, 27, 73, 75, 78, 28, 29, 88, 91, 32, 33, 103, 35, 114, 40, 120, 47, 48, 136, 57, 142, 68, 157, 160, 62, 83, 112, 113, 214, 217, 116, 223, 135, 26, 156, 43, 158, 41, 40, 161, 59, 259, 260, 104, 103

Offset: 1

Author

Zak Seidov, May 05 2005

Keywords

• nonn
• less

Examples

			a(10)=34 because 10*prime(10)+34 = 10*29+34 = 324 = 18^2.
		

Crossrefs

Cf. A033286 (n*prime(n)), A080883 (distance of n to next square).

Programs

Mathematica

a[n_]:=(Floor[Sqrt[n*Prime[n]]]+1)^2-n*Prime[n]
lnk[n_]:=With[{c=n Prime[n]},(Floor[Sqrt[c]]+1)^2-c]; Array[lnk,70] (* Harvey P. Dale, Feb 17 2024 *)

Formula

a(n) = (floor(sqrt(n*prime(n)))+1)^2 - n*prime(n).

a(n) = A080883(A033286(n)). - Michel Marcus, Mar 29 2020