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A155136 Integers n such that n+28 is a square. 4
-28, -27, -24, -19, -12, -3, 8, 21, 36, 53, 72, 93, 116, 141, 168, 197, 228, 261, 296, 333, 372, 413, 456, 501, 548, 597, 648, 701, 756, 813, 872, 933, 996, 1061, 1128, 1197, 1268, 1341, 1416, 1493, 1572, 1653, 1736, 1821, 1908, 1997, 2088, 2181, 2276, 2373 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Values x of nonzero solutions (x, y) to the Diophantine equation x^3+28*x^2 = y^2. Corresponding values y are in A155137.
Agrees with A155135 except for omission of zero after a(6) = 3.
LINKS
FORMULA
a(n) = n^2-2*n-27.
G.f.: -(4-3*x)*(7-9*x)/(1-x)^3.
EXAMPLE
For n = -19, n+28 = 9 = 3^2 is a square; for n = -3, n+28 = 25 = 5^2 is a square; for n = 21, n+28 = 49 = 7^2 is a square.
MATHEMATICA
Range[0, 50]^2-28 (* or *) LinearRecurrence[{3, -3, 1}, {-28, -27, -24}, 50] (* Harvey P. Dale, May 15 2023 *)
PROG
(Magma) [ n: n in [ -30..2500] | IsSquare(n+28) ];
(PARI) a(n)=n^2-2*n-27 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A196028 A291161 A155135 * A022984 A023470 A343008
KEYWORD
sign,easy
AUTHOR
Klaus Brockhaus, Jan 21 2009
STATUS
approved

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Last modified July 12 09:57 EDT 2024. Contains 374239 sequences. (Running on oeis4.)