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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

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

(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. A002328, A088502, A110013, A003601, A000217, A028387.

Cf. A010051.

Sequence in context: A106071 A073847 A024833 * A078179 A045451 A338566

Adjacent sequences: A002324 A002325 A002326 * A002328 A002329 A002330

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended by Ray Chandler, Sep 07 2005

STATUS

approved

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Last modified December 7 16:10 EST 2022. Contains 358667 sequences. (Running on oeis4.)