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Search: id:A159351
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| A159351 |
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a(k) = minimal prime in representation m^2+n^2 from sequence A159296 |
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+0
1
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| 5, 13, 29, 41, 61, 89, 113, 149, 181, 233, 269, 313, 389, 421, 521, 557, 613, 709, 761, 853, 929, 1013, 1109, 1201, 1301, 1409, 1553, 1637, 1741, 1861, 1997, 2113, 2269, 2381, 2521, 2677, 2837, 2969, 3121, 3461, 3449, 3613, 3797, 4001, 4153, 4337, 4513, 4729, 5081
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OFFSET
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1,1
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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
R. K. Guy, Unsolved Problems in Number Theory (2nd ed.) New York: Springer-Verlag, 1994
David Wells, Prime Numbers: The Most Mysterious Figures in Math. John Wiley and Sons. 2005
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FORMULA
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1) m and n are necessarily relative prime for m^2+n^2 prime
2) Case m+n=2 (even) with 1^2+1^2=2 is excluded
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EXAMPLE
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1) 1^2+2^2=5=a(1)=1
2) 2^2+3^2=13=a(2) < 1^2+4^2=17
3) 2^2+5^2=29=a(3) < 1^2+6^2=37
4) 23^2+32^2=1553=a(27) < 1597, 1657, 1693, 1733, 1777, 1877, 1933, 1993, 2273, 2437, 2617, 2713, 2917, 14 prime representations as sum of two squares
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CROSSREFS
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A159296, A145354, A157884
Sequence in context: A078598 A155054 A158756 this_sequence A163251 A146286 A065374
Adjacent sequences: A159348 A159349 A159350 this_sequence A159352 A159353 A159354
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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 11 2009
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EXTENSIONS
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A-number in definition and cross-ref. corrected, and more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 24 2009
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