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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A002144, A309812.

Sequence in context: A202004 A020249 A287391 * A296304 A156159 A099011

Adjacent sequences:  A325418 A325419 A325420 * A325422 A325423 A325424

KEYWORD

nonn

AUTHOR

Mohsin A. Shaikh, Sep 06 2019

EXTENSIONS

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

STATUS

approved

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Last modified October 27 00:02 EDT 2021. Contains 348270 sequences. (Running on oeis4.)