cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Mohsin A. Shaikh

Mohsin A. Shaikh's wiki page.

Mohsin A. Shaikh has authored 2 sequences.

A325421 Numbers k coprime to 10 such that there are exactly two values of A for which k^2+4*A and k^2-4*A are perfect squares.

Original entry on oeis.org

169, 289, 507, 841, 867, 1183, 1369, 1521, 1681, 1859, 2023, 2523, 2601, 2809, 3179, 3211, 3549, 3721, 3887, 4107, 4563, 5043, 5239, 5329, 5491, 5577, 5887, 6069, 6647, 7267, 7569, 7803, 7921, 7943, 8281, 8427, 8959, 9251, 9409, 9537, 9583, 9633, 9971
Offset: 1

Views

Author

Mohsin A. Shaikh, Sep 06 2019

Keywords

Comments

These are the odd integers k, not a multiple of 5, such that k^2 is an arithmetic mean of two other odd perfect squares in exactly two ways.

Examples

			169 is a term since 169^2±4*(5070) and 169^2±4*(7140) are all perfect squares.

Crossrefs

Cf. A002144, A309812.

Programs

  • PARI
    ok(k)={if(k%2==0||k%5==0, 0, my(k2=k^2, L=List()); forstep(i=1, k-1, 2, my(d=k2-i^2); if(issquare(k2+d), listput(L,i))); #L==2)}
for(k=1, 10000, if(ok(k), print1(k, ", "))) \\ Andrew Howroyd, Sep 06 2019

Extensions

a(28)-a(43) from Andrew Howroyd, Sep 06 2019

A309812 Odd integers k such that k^2 is arithmetic mean of two other perfect squares.

Original entry on oeis.org

5, 13, 15, 17, 25, 29, 35, 37, 39, 41, 45, 51, 53, 55, 61, 65, 73, 75, 85, 87, 89, 91, 95, 97, 101, 105, 109, 111, 113, 115, 117, 119, 123, 125, 135, 137, 143, 145, 149, 153, 155, 157, 159, 165, 169, 173, 175, 181, 183, 185, 187, 193, 195, 197, 203, 205, 215, 219
Offset: 1

Views

Author

Mohsin A. Shaikh, Aug 18 2019

Keywords

Examples

			5 is a term because 5^2 = 25 = (1^2 + 7^2)/2.

Crossrefs

Intersection of A005408 and A009003.

Programs

  • Mathematica
    Select[Range[1, 300, 2], SquaresR[2, 2 #^2] > 4 &] (* Giovanni Resta, Aug 18 2019 *)
  • PARI
    isok(n) = {if (n %2, for (i=1, n, x = 2*n^2-i^2; if ((x!=i^2) && (x>0) && issquare(x), return (i));););} \\ Michel Marcus, Aug 18 2019

Extensions

More terms from Giovanni Resta, Aug 18 2019

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