A002650 Quintan primes: p = (x^5 + y^5)/(x + y). (Formerly M4792 N2044)

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

1,1

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

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]

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A002649.

Sequence in context: A199326 A078554 A189227 * A060884 A141935 A222408

Adjacent sequences: A002647 A002648 A002649 * A002651 A002652 A002653

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, May 08 2014

Status

approved