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

1,1

Links

Table of n, a(n) for n=1..66.

Formula

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A078298 A096063 A101281 * A121634 A006015 A301332

Adjacent sequences: A106030 A106031 A106032 * A106034 A106035 A106036

Keyword

nonn,less

Author

Zak Seidov, May 05 2005

Status

approved