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A002973
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a(n) is half of the even member of {x,y}, where x^2+y^2 is the n-th prime of the form 4i+1.
(Formerly M0135)
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7
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1, 1, 2, 1, 3, 2, 1, 3, 4, 4, 2, 5, 5, 4, 2, 5, 3, 1, 5, 6, 7, 1, 4, 2, 8, 5, 7, 8, 1, 6, 7, 8, 9, 4, 9, 5, 3, 10, 10, 7, 6, 10, 2, 5, 11, 10, 5, 7, 10, 12, 4, 12, 9, 8, 2, 11, 3, 6, 13, 13, 11, 1, 13, 10, 6, 11, 13, 14, 7, 5, 9, 2, 3, 8, 10, 12, 5, 14, 2, 3, 14, 11, 15, 16, 16, 5, 15, 1, 8, 11
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is odd iff x^2+y^2==5(mod 8). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jul 12 2009]
A002972(n)^2 + 4*a(n)^2 = A002144(n); A002331(n+1)=MIN(A002972(n),2*a(n)) and A002330(n+1)=MAX(A002972(n),2*a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2010]
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REFERENCES
| E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, Gordon and Breach, NY, 1971, p. 243.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).
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FORMULA
| a(n) = MIN(A173331(n), A002144(n) - A173331(n)) / 2. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2010]
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EXAMPLE
| The 3rd prime of the form 4i+1 is 17=1^2+4^2, so a(3)=4/2=2.
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CROSSREFS
| Cf. A002144, A002972.
Sequence in context: A195079 A124458 A199538 * A071476 A071499 A039953
Adjacent sequences: A002970 A002971 A002972 * A002974 A002975 A002976
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Mar 05 2003
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