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

1,3

Links

Table of n, a(n) for n=1..94.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A256243.

Sequence in context: A130659 A083741 A258761 * A173004 A118343 A309148

Adjacent sequences: A256242 A256243 A256244 * A256246 A256247 A256248

Keyword

nonn,easy

Author

Zak Seidov, Mar 20 2015

Status

approved