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Numbers k such that (k^2 + k + 1)/3 is prime.
(Formerly M3301 N1331)
2

%I M3301 N1331 #34 Oct 17 2023 08:19:10

%S 4,7,10,13,19,28,31,34,40,43,52,70,73,76,82,85,91,97,103,112,115,124,

%T 127,136,145,148,157,166,175,187,190,199,202,223,241,244,259,265,271,

%U 274,280,286,316,325,358,370,376,385,388,409,421,427,442,460,469,472

%N Numbers k such that (k^2 + k + 1)/3 is prime.

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A002640/b002640.txt">Table of n, a(n) for n = 1..1000</a>

%H A. J. C. Cunningham, <a href="/A001912/a001912.pdf">Binomial Factorisations</a>, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]

%t Select[Range[500], PrimeQ[(#^2 + # + 1)/3] &] (* _Vincenzo Librandi_, Sep 25 2012 *)

%o (Magma) [n: n in [4..500] | IsPrime((n^2+n+1) div 3)]; // _Vincenzo Librandi_, Nov 18 2010

%o (PARI) is(n)=isprime((n^2+n+1)/3) \\ _Charles R Greathouse IV_, Jun 06 2017

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified September 20 16:50 EDT 2024. Contains 376075 sequences. (Running on oeis4.)