A256245 a(n) is the smallest positive number m such that n+3*m is a square, or 0 if no such m exists.

1, 0, 2, 4, 0, 1, 3, 0, 9, 2, 0, 8, 1, 0, 7, 3, 0, 6, 2, 0, 5, 1, 0, 4, 8, 0, 3, 7, 0, 2, 6, 0, 1, 5, 0, 15, 4, 0, 14, 3, 0, 13, 2, 0, 12, 1, 0, 11, 5, 0, 10, 4, 0, 9, 3, 0, 8, 2, 0, 7, 1, 0, 6, 12, 0, 5, 11, 0, 4, 10, 0, 3, 9, 0, 2, 8, 0, 1, 7, 0, 21, 6, 0, 20, 5, 0, 19, 4, 0, 18, 3, 0, 17, 2

Offset: 1

Author

Zak Seidov, Mar 20 2015

Keywords

• nonn
• easy

Examples

			1 + 3*1 = 4 = 2^2, 3 + 3*2 = 9 = 3^2, 4 + 3*4 = 16 = 4^2.
		

Crossrefs

Cf. A256243.

Programs

Mathematica

Table[m = 1; If[Mod[n, 3] == 2, m = 0, While[! IntegerQ[Sqrt[n + 3*m]], m++]]; m, {n, 100}] (* Michael De Vlieger, Mar 20 2015 *)

PARI

a(n)=if(n==Mod(2,3),return(0));m=1;while(!issquare(n+3*m),m++);m
vector(100,n,a(n)) \\ Derek Orr, Mar 22 2015

Formula

a(n)=0 iff n==2 mod 3 because 2 is quadratic nonresidue of 3.