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Search: id:A002645
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| A002645 |
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Quartan primes: primes of the form x^4 + y^4, x>0, y>0.
(Formerly M5042 N2178)
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+0
5
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| 2, 17, 97, 257, 337, 641, 881, 1297, 2417, 2657, 3697, 4177, 4721, 6577, 10657, 12401, 14657, 14897, 15937, 16561, 28817, 38561, 39041, 49297, 54721, 65537, 65617, 66161, 66977, 80177, 83537, 83777, 89041, 105601, 107377, 119617, 121937
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes in the set {A000583 + A000583}. This is a subset of prime sums of two squares (2 and the real Gaussian primes). - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
N. D. Elkies, Primes of the form a^4 + b^4, Mathematical Buds, Ed. H. D. Ruderman Vol. 3 Chap. 3 pp. 22-8 Mu Alpha Theta 1984.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
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A000040 INTERSECTION A003336. - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
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EXAMPLE
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a(1) = 2 = 1^4 + 1^4.
a(2) = 17 = 1^4 + 2^4.
a(3) = 97 = 2^4 + 3^4.
a(4) = 257 = 1^4 + 4^4.
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MATHEMATICA
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lst={}; Do[Do[p=n^4+m^4; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!}], {m, 0, 5!}]; lst; Length[lst]; Take[Union[lst], 123] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 21 2009]
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CROSSREFS
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Cf. A002646, A000040, A000583, A003336.
Sequence in context: A079889 A053786 A081744 this_sequence A100268 A163790 A129123
Adjacent sequences: A002642 A002643 A002644 this_sequence A002646 A002647 A002648
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Nov 07 2002
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