A201917 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+84847)^2 = y^2.

0, 2085, 2325, 5253, 6141, 6293, 7728, 10013, 11960, 12920, 14637, 16940, 17112, 18737, 21648, 21948, 23541, 24633, 26588, 27716, 31620, 33012, 34937, 35145, 38012, 40641, 42716, 44268, 47633, 49848, 52785, 54237, 56420, 56840, 60605, 63828, 67541, 70448

Offset

1,2

Comments

Note that 84847 = 7 * 17 * 23 * 31, the first four primes in A058529.

Links

Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 159 terms from Vincenzo Librandi)

Formula

a(n) = a(n-1) + 6*a(n-81) - 6*a(n-82) - a(n-162) + a(n-163), where the 163 initial terms can be computed using the Mathematica program. The initial terms begin with 0 and end with 1696940.

Mathematica

d = 84847; t = Select[Range[0, 68000], IntegerQ[Sqrt[#^2 + (#+d)^2]] &]

Crossrefs

Cf. A201916 (has list of all such sequences).

Sequence in context: A323471 A251225 A306421 * A250076 A255146 A293106

Adjacent sequences: A201914 A201915 A201916 * A201918 A201919 A201920

Keyword

nonn

Author

T. D. Noe, Feb 09 2012

Status

approved