A002642 -id:A002642 - cp's OEIS frontend

A002643 Numbers k such that (k^2 + k + 1)/19 is prime.

7, 11, 26, 45, 83, 125, 140, 182, 197, 201, 216, 239, 258, 311, 330, 353, 444, 467, 482, 486, 524, 539, 558, 600, 752, 771, 843, 881, 885, 923, 980, 999, 1071, 1113, 1170, 1223, 1337, 1356, 1470, 1664, 1835, 1869, 1911, 1949, 1968, 2021, 2078, 2120, 2192

Offset: 1

N. J. A. Sloane

A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
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).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]

Cf. A002640, A002641, A002642, A002644.

Select[Range[2500], PrimeQ[(#^2 + # + 1)/19] &] (* Vincenzo Librandi, Sep 25 2012 *)

is(n)=isprime((n^2+n+1)/19) \\ Charles R Greathouse IV, Jun 06 2017

More terms from Jon E. Schoenfield, May 06 2010

A272629 Primes p such that (p^2 + p + 1)/13 is prime.

Original entry on oeis.org

29, 113, 419, 503, 659, 887, 1277, 1361, 1433, 2141, 2213, 2687, 3851, 4007, 4397, 4787, 5333, 5417, 5573, 7127, 7757, 7829, 8609, 8693, 8849, 9161, 9311, 9623, 10247, 10487, 11261, 11423, 12197, 12743, 13217, 13523, 14537, 14621, 14771, 15083, 15161

Offset: 1

Vincenzo Librandi, May 04 2016

nonn

Primes in A002642.

			a(1) = 29 because (29^2+29+1)/13 = 67 is a prime.

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A002642.

Select[Prime[Range[5000]], PrimeQ[(#^2 + # + 1) / 13] &]

lista(nn) = {forprime(p=2, nn, if ((denominator(q=(p^2 + p + 1)/13)== 1) && isprime(q), print1(p, ", ")););} \\ Michel Marcus, May 05 2016

cp's OEIS Frontend

A002643 Numbers k such that (k^2 + k + 1)/19 is prime.

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