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A002650
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Quintan primes: p = (x^5 + y^5)/(x + y).
(Formerly M4792 N2044)
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2
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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
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OFFSET
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1,1
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COMMENTS
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(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
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REFERENCES
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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).
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LINKS
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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]
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EXAMPLE
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(3^5 + 1^5)/(3 + 1) = 61. This is prime and therefore in the sequence. - Jens Kruse Andersen, Jul 14 2014
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MATHEMATICA
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Take[Select[Union[(#[[1]]^5+#[[2]]^5)/Total[#]&/@Tuples[Range[200], 2]], #>0&& PrimeQ[#]&], 50] (* Harvey P. Dale, May 21 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A002649.
Sequence in context: A199326 A078554 A189227 * A060884 A141935 A222408
Adjacent sequences: A002647 A002648 A002649 * A002651 A002652 A002653
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Sean A. Irvine, May 08 2014
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STATUS
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approved
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