

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
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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^22*n27.
G.f.: (43*x)*(79*x)/(1x)^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]^228 (* 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) ];


CROSSREFS



KEYWORD

sign,easy


AUTHOR



STATUS

approved



