login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117951 a(n) = n^2 + 5. 13
5, 6, 9, 14, 21, 30, 41, 54, 69, 86, 105, 126, 149, 174, 201, 230, 261, 294, 329, 366, 405, 446, 489, 534, 581, 630, 681, 734, 789, 846, 905, 966, 1029, 1094, 1161, 1230, 1301, 1374, 1449, 1526, 1605, 1686, 1769, 1854, 1941, 2030, 2121, 2214, 2309, 2406, 2505 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Near-Square Prime

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

FORMULA

a(n) = 2*n + a(n-1) - 1 (with a(0)=5). - Vincenzo Librandi, Nov 13 2010

From Colin Barker, Apr 10 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (5-9*x+6*x^2)/(1-x)^3. (End)

From Amiram Eldar, Jul 13 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(5)*Pi*coth(sqrt(5)*Pi))/10.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(5)*Pi*cosech(sqrt(5)*Pi))/10. (End)

MATHEMATICA

lst={}; Do[AppendTo[lst, n^2+5], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)

Range[0, 50]^2+5 (* or *) LinearRecurrence[{3, -3, 1}, {5, 6, 9}, 60] (* Harvey P. Dale, Aug 04 2020 *)

PROG

(sage) [lucas_number1(3, n, -5) for n in range(0, 51)] # Zerinvary Lajos, May 16 2009

(PARI) a(n)=n^2+5 \\ Charles R Greathouse IV, Apr 10 2012

CROSSREFS

For numbers n such that n^2 + 5 is prime, see A078402.

Sequence in context: A301658 A286338 A344231 * A328115 A327975 A227611

Adjacent sequences: A117948 A117949 A117950 * A117952 A117953 A117954

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 04 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)