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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002327 Primes of the form k^2 - k - 1.
(Formerly M3810 N1558)
41
5, 11, 19, 29, 41, 71, 89, 109, 131, 181, 239, 271, 379, 419, 461, 599, 701, 811, 929, 991, 1259, 1481, 1559, 1721, 1979, 2069, 2161, 2351, 2549, 2861, 2969, 3079, 3191, 3539, 3659, 4159, 4289, 4421, 4691, 4969, 5851, 6971, 7309, 7481, 8009, 8741, 8929 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also primes of form x*y + x + y or x*y - x - y, where x and y are two successive numbers. - Giovanni Teofilatto, May 12 2004
Equivalently primes p such that 4p+5 is square. - Giovanni Teofilatto, Sep 03 2005
Arithmetic numbers which are triangular, A003601(p)=A000217(k), p prime. sigma_1(p)/sigma_0(p) = k*(k+1)/2; sigma_r(p) divisor function, p prime, k integer. - Ctibor O. Zizka, Jul 14 2008
Also primes of the form k^2 + 3k + 1 (primes in A028387). - Zak Seidov, Apr 13 2014
Also primes p such that the sum of divisors (A000203) of p is oblong (A002378). - Michel Marcus, Jan 09 2015
REFERENCES
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
L. Poletti, Tavole di Numeri Primi Entro Limiti Diversi e Tavole Affini, Milan, 1920, p. 249.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi and Pierre CAMI, Table of n, a(n) for n = 1..10000 (Vincenzo Librandi to n=1000)
Marie Euler and Christophe Petit, Expanding the use of quasi-subfield polynomials, arXiv:1909.11326 [cs.CR], 2019.
FORMULA
a(n) = A002328(n)^2 - A002328(n) - 1 = (A110013(n) - 5)/4. - Ray Chandler, Sep 07 2005
a(n) >> n^2 log n by Brun's sieve. - Charles R Greathouse IV, Oct 10 2023
MAPLE
A002327:=n->`if`(isprime(n^2-n-1), n^2-n-1, NULL): seq(A002327(n), n=1..100); # Wesley Ivan Hurt, Aug 09 2014
MATHEMATICA
Select[Table[n^2-n-1, {n, 100}], PrimeQ] (* Harvey P. Dale, May 03 2011 *)
PROG
(PARI) for(n=2, 1e3, if(isprime(k=n^2-n-1), print1(k", "))) \\ Charles R Greathouse IV, Jul 31 2011
(PARI) list(lim)=my(v=List(), p); forstep(n=5, sqrtint(4*lim+5), 2, if(isprime(p=(n^2-5)/4), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Oct 10 2023
(Magma) [ a: n in [0..150] | IsPrime(a) where a is n^2 - n - 1 ]; // Vincenzo Librandi, Aug 01 2011
(Haskell)
a002327 n = a002327_list !! (n-1)
a002327_list = filter ((== 1) . a010051') a028387_list
-- Reinhard Zumkeller, Jul 17 2014
CROSSREFS
Cf. A010051.
Sequence in context: A106071 A073847 A024833 * A078179 A045451 A338566
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended by Ray Chandler, Sep 07 2005
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 March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)