A256243 -id:A256243 - cp's OEIS frontend

A256244 a(n) = sqrt(n + 2*A256243(n)).

3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 12

Offset: 1

Zak Seidov, Mar 20 2015

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000196, A256243.

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

a(n)=m=1;while(!issquare(n+2*m),m++);sqrt(n+2*m)
vector(100,n,round(a(n))) \\ Derek Orr, Mar 22 2015

a(n)=my(s=sqrtint(n)); if((s-n)%2,s+1,s+2) \\ Charles R Greathouse IV, Mar 23 2015

sqrt(n) < a(n) <= sqrt(n) + 2. - Charles R Greathouse IV, Mar 23 2015

A253203 The least square larger than n with same parity as n.

Original entry on oeis.org

9, 4, 9, 16, 9, 16, 9, 16, 25, 16, 25, 16, 25, 16, 25, 36, 25, 36, 25, 36, 25, 36, 25, 36, 49, 36, 49, 36, 49, 36, 49, 36, 49, 36, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100

Offset: 1

Tom Edgar and Zak Seidov, Mar 25 2015

			9 is the least odd square > 1;
4 is the least even square > 2;
9 is the least odd square > 3.

Cf. A256243, A256244.

f[n_] := Block[{s = If[n == 1, Range[3]^2, Range[2 Ceiling@ Sqrt@ n]^2]}, If[EvenQ@ n, SelectFirst[s, EvenQ@ # && # > n &], SelectFirst[s, OddQ@ # && # > n &]]]; Array[f, 120] (* Michael De Vlieger, Mar 25 2015 *)

A = []
for i in [1..100]:
    for y in [1..100]:
        x = y**2
        if x>i and (x-i)%2==0:
            A.append(x)
            break
A

a(n) = A256244(n)^2 = n + 2*A256243(n).

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

Original entry on oeis.org

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

Zak Seidov, Mar 20 2015

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

Cf. A256243.

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 *)

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

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

cp's OEIS Frontend

A256244 a(n) = sqrt(n + 2*A256243(n)).

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A253203 The least square larger than n with same parity as n.

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

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Author

Keywords

Examples

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Mathematica

PARI

Formula