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Search: id:A057368
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| A057368 |
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Number of Gaussian primes (in the first half quadrant; i.e. 0 to 45 degrees) with real part = n. |
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+0
2
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| 1, 1, 2, 1, 2, 2, 2, 3, 1, 4, 3, 1, 4, 3, 3, 3, 4, 3, 5, 6, 2, 4, 6, 3, 7, 6, 4, 4, 4, 4, 8, 6, 5, 6, 8, 5, 6, 7, 3, 9, 5, 5, 9, 8, 7, 9, 7, 7, 10, 8, 6, 9, 10, 5, 8, 8, 6, 10, 12, 8, 11, 10, 6, 9, 15, 5, 11, 11, 4, 11, 14, 6, 12, 10, 12, 11, 9, 8, 12, 19, 10, 15, 10, 8, 19, 11, 8, 11, 14, 15, 13
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Conjecture: a(n)>0 for all n>0. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
The graph of this sequence inspires the following conjecture: A > a(n)/pi(n) > B, where A and B are constants and pi(n) is the prime counting function (A000720). - T. D. Noe (noe(AT)sspectra.com), Feb 26 2007
Stronger conjecture: Let pi(n) be the prime counting function (A000720). Then pi(n) >= a(n) >= pi(n)/5 for n>1, with the following equalities: pi(2)=a(2), pi(3)=a(3), pi(10)=a(10) and a(12)=pi(12)/5. - T. D. Noe (noe(AT)sspectra.com), Feb 26 2007
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REFERENCES
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Mark A. Herkommer, "Number Theory, A Programmer's Guide," McGraw-Hill, New York, 1999, page 269.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Index entries for Gaussian integers and primes
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FORMULA
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a(n) = A069004(n) + 1 if n is 1 or a prime = 3 (mod 4), A069004(n) otherwise. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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MATHEMATICA
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Do[ c=0; Do[ If[ PrimeQ[ j + k*I, GaussianIntegers -> True ], c++ ], {j, n, n}, {k, 0, j} ]; Print[ c ], {n, 1, 75} ]
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CROSSREFS
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Cf. A055683 and A057352.
Cf. A069004.
Sequence in context: A065531 A131840 A144590 this_sequence A085033 A096446 A008677
Adjacent sequences: A057365 A057366 A057367 this_sequence A057369 A057370 A057371
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 22 2000
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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