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A126665
a(n) = -n^2 + 9*n + 53.
5
53, 61, 67, 71, 73, 73, 71, 67, 61, 53, 43, 31, 17, 1, -17, -37, -59, -83, -109, -137, -167, -199, -233, -269, -307, -347, -389, -433, -479, -527, -577, -629, -683, -739, -797, -857, -919, -983, -1049, -1117, -1187, -1259, -1333, -1409, -1487, -1567, -1649, -1733, -1819, -1907, -1997, -2089, -2183, -2279
OFFSET
0,1
COMMENTS
Quadratic equation derived from the four primes 61, 67, 71, 73 using the method of common differences. Many of the initial terms are primes.
FORMULA
From Arkadiusz Wesolowski, Oct 24 2013: (Start)
a(n) = -A186950(n+19).
G.f.: (53 - 98*x + 43*x^2)/(1 - x)^3. (End)
From Elmo R. Oliveira, Nov 02 2024: (Start)
E.g.f.: (53 + 8*x - x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
EXAMPLE
For n=8, -1*8^2 + 9*8 + 53 = 61.
MATHEMATICA
Table[ - n^2 + 9*n + 53, {n, 0, 46}] (* Arkadiusz Wesolowski, Oct 24 2013 *)
LinearRecurrence[{3, -3, 1}, {53, 61, 67}, 60] (* Harvey P. Dale, Apr 04 2024 *)
PROG
(PARI) a(n) = -n^2 + 9*n + 53 \\ Michel Marcus, Jun 30 2013
(Magma) [-n^2+9*n+53 : n in [0..46]]; // Arkadiusz Wesolowski, Oct 24 2013
CROSSREFS
Cf. A186950.
Sequence in context: A180553 A079593 A086082 * A279191 A107160 A075587
KEYWORD
sign,easy,changed
AUTHOR
Michael M. Ross, Mar 13 2007
STATUS
approved