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Search: id:A159829
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| A159829 |
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a(n) is the smallest natural number m such that n^3+m^3+1^3 is prime. |
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+0
7
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| 1, 2, 1, 2, 1, 4, 15, 2, 3, 2, 11, 10, 9, 2, 7, 14, 5, 4, 9, 2, 15, 2, 7, 16, 15, 8, 13, 2, 1, 10, 3, 4, 15, 2, 11, 10, 9, 2, 7, 6, 13, 22, 5, 2, 1, 6, 29, 10, 29, 10, 3, 2, 11, 12, 3, 8, 3, 2, 19, 6, 15, 8, 1, 2, 1, 18, 5, 2, 1, 18, 1, 12, 17, 14, 15, 26, 7, 6, 3, 2, 19, 12, 1, 18, 3, 8, 15, 2, 11, 6
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OFFSET
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1,2
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COMMENT
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1) a(2k-1) is odd, a(2k) is even.
2) Exponent 2: There are infinitely many primes of the forms n^2+m^2 and n^2+m^2+1^2.
3) Exponent k>2: Are there infinitely many primes of the forms n^k+m^k and n^k+m^k+1^k?
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, Vol, I: Divisibility and Primality, AMS Chelsea Publ., 1999
A. Weil, Number theory: an approach through history, Birkhauser 1984
David Wells, Prime Numbers: The Most Mysterious Figures in Math. John Wiley and Sons. 2005
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EXAMPLE
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2^3+2^3+1=17 = A000040(7); a(2)=2.
7^3+15^3+1=3719 = A000040(519); a(7)=15.
21^3+15^3+1=18523 = A000040(2122), a(21)=15.
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MAPLE
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A159829 := proc(n) for m from 1 do if isprime(n^3+m^3+1) then RETURN(m) ; fi; od: end: seq(A159829(n), n=1..120) ; # R. J. Mathar ((mathar(AT)strw.leidenuniv.nl), Apr 28 2009
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CROSSREFS
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Cf. A069003, A159828
Sequence in context: A106380 A076198 A032021 this_sequence A128515 A119569 A066083
Adjacent sequences: A159826 A159827 A159828 this_sequence A159830 A159831 A159832
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 23 2009
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2009
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