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Search: id:A099807
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| A099807 |
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If a,b are prime numbers satisfying the Diophantine equation a^3+b^3=c^2, then a is -1 mod 12 and b is 1 mod 12, or vice versa. Choose 'b' to be 1 mod 12. This is the sequence of 'b' values, sorted by the magnitude of c. |
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+0
5
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| 37, 2137, 8929, 1801, 48817, 6637, 57241, 133597, 151477, 334717, 3889, 127717, 786697, 735781, 1154017, 38557, 1662229, 2446777, 3882661, 3811669, 2747449, 3716701, 5634637, 3600097, 9836221, 10591849, 7139569, 9473161, 11395309
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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All terms of this sequence are of the form -3*M^4+N^4+6*M^2*N^2 for some pair M,N of relatively prime positive integers of opposite parity. For each n, a=A099806[n], b=A099807[n] are prime numbers and a^3 + b^3 = c^2, for some integer c. c is divisible by 12 and A098970 gives the values of c/12.
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LINKS
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James Buddenhagen, Two Primes Cubed which Sum to a Square.
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EXAMPLE
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37 is in the sequence because 37 is a prime congruent to 1 mod 12 and 11^3+37^3=228^2.
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CROSSREFS
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Cf. A099806, A098970, A099808, A099809.
Sequence in context: A130013 A088872 A025762 this_sequence A141087 A105839 A074992
Adjacent sequences: A099804 A099805 A099806 this_sequence A099808 A099809 A099810
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KEYWORD
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nonn
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AUTHOR
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James Buddenhagen (jbuddenh(AT)gmail.com), Oct 26 2004
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