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A126665 a(n) = -n^2 + 9n + 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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..53.

Michael M. Ross, Natural Numbers

Robert Sacks, Number Spiral: Method of Common Differences

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

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 *)

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

Sequence in context: A180553 A079593 A086082 * A279191 A107160 A075587

Adjacent sequences:  A126662 A126663 A126664 * A126666 A126667 A126668

KEYWORD

sign,easy

AUTHOR

Michael M. Ross, Mar 13 2007

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)