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A091295
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(Number of primes == 3 mod 4 less than 10^n) - (number of primes == 1 mod 4 less than 10^n).
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3
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1, 2, 7, 10, 25, 147, 218, 446, 551, 5960, 14252, 63337, 118472, 183457, 951700, 3458334, 6284060, 2581691, 80743228, 259753425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Deleglise, Marc; Dusart, Pierre; and Roblot, Xavier-Francois, Counting primes in residue classes. Math. Comp. 73 (2004), 1565-1575.
Hans Riesel, Prime Numbers and Computer Methods for Factorization, 2nd ed., Birkhauser, The distribution of primes between the two series 4n+1 and 4n+3, pages 73-77, with graphs.
Carlos Rivera, Puzzle 256, Jack Brennen old records (www.primepuzzles.net/puzzles/puzz_256.htm)
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FORMULA
| a(n) = A091099(n) - A091098(n) = A093153(n) + 1 [From Max Alekseyev (maxale(AT)gmail.com), May 17 2009]
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EXAMPLE
| a(1) = 1 because below 10^1 3 and 7 are 3 mod 4 and 5 is 1 mod 4 and the difference is 2-1=1.
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CROSSREFS
| Cf. A091098, A091099. A002144, A002145, A091318, A091267.
Sequence in context: A066964 A066967 A032007 * A084184 A015963 A056656
Adjacent sequences: A091292 A091293 A091294 * A091296 A091297 A091298
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KEYWORD
| nonn
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net), Feb 23 2004
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EXTENSIONS
| a(17)-a(20) from Marc Deleglise (marc.deleglise(AT)math.univ-lyon1.fr), Jun 28 2007
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