A002650 Quintan primes: p = (x^5 + y^5)/(x + y).

11, 61, 181, 421, 461, 521, 991, 1621, 1871, 3001, 4441, 4621, 6871, 9091, 9931, 12391, 13421, 14821, 19141, 25951, 35281, 35401, 55201, 58321, 61681, 62071, 72931, 74731, 91331, 92921, 95881, 108421, 117911, 117991, 131041, 132661, 141961

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

(x^5 + y^5)/(x + y) = x^4 - y*x^3 + y^2*x^2 - y^3*x + y^4. - Jens Kruse Andersen, Jul 14 2014

Examples

			(3^5 + 1^5)/(3 + 1) = 61. This is prime and therefore in the sequence. - _Jens Kruse Andersen_, Jul 14 2014
		

References

• A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 2, p. 201.
• 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

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
• A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]

Crossrefs

Cf. A002649.

Programs

Mathematica

Take[Select[Union[(#[[1]]^5+#[[2]]^5)/Total[#]&/@Tuples[Range[200],2]], #>0&& PrimeQ[#]&],50] (* Harvey P. Dale, May 21 2012 *)

PARI

m=10^6; v=[]; for(x=1, (2*m)^(1/4), for(y=1, x, n=(x^5+y^5)/(x+y); if(n<=m && isprime(n), v=concat(v,n)))); vecsort(v) \\ Jens Kruse Andersen, Jul 14 2014

Extensions

More terms from Sean A. Irvine, May 08 2014