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Quintan primes: p = (x^5 - y^5)/(x - y).
(Formerly M3964 N1636)
4

%I M3964 N1636 #32 Oct 18 2023 05:00:32

%S 5,31,211,1031,2801,4651,5261,6841,8431,14251,17891,20101,21121,22621,

%T 22861,26321,30941,33751,36061,41141,46021,48871,51001,58411,61051,

%U 88741,92821,103801,109141,114641,118061,125591,170101,176641,209801

%N Quintan primes: p = (x^5 - y^5)/(x - y).

%C 5 is a term because x^4 + y*x^3 + y^2*x^2 + y^3*x + y^4 = 5 when x=y=1. - _N. J. A. Sloane_, May 12 2014

%D A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 2, p. 200.

%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 Jens Kruse Andersen, <a href="/A002649/b002649.txt">Table of n, a(n) for n = 1..10000</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]

%o (PARI) m=10^6; v=[5]; for(x=1, m^(1/4), for(y=1, x-1, n=(x^5-y^5)/(x-y); if(n<=m && isprime(n), v=concat(v,n)))); vecsort(v) \\ _Jens Kruse Andersen_, Jul 14 2014

%Y Cf. A002650.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E a(26)-a(35) from _Sean A. Irvine_, May 08 2014