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A002972
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a(n) is the odd member of {x,y}, where x^2+y^2 is the n-th prime of the form 4i+1.
(Formerly M2221)
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8
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1, 3, 1, 5, 1, 5, 7, 5, 3, 5, 9, 1, 3, 7, 11, 7, 11, 13, 9, 7, 1, 15, 13, 15, 1, 13, 9, 5, 17, 13, 11, 9, 5, 17, 7, 17, 19, 1, 3, 15, 17, 7, 21, 19, 5, 11, 21, 19, 13, 1, 23, 5, 17, 19, 25, 13, 25, 23, 1, 5, 15, 27, 9, 19, 25, 17, 11, 5, 25, 27, 23, 29, 29, 25, 23, 19, 29, 13, 31, 31
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)^2 + 4*A002973(n)^2 = A002144(n); A002331(n+1)=MIN(a(n),2*A002973(n)) and A002330(n+1)=MAX(a(n),2*A002973(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2010]
It appears that the terms in this sequence are the absolute values of the terms in A046730. [Gerry Myerson, Dec 02 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(A173330(n), A002144(n) - A173330(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2010]
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EXAMPLE
| The 2nd prime of the form 4i+1 is 13=2^2+3^2, so a(2)=3.
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CROSSREFS
| Cf. A002144, A002973.
Sequence in context: A114567 A001051 A046730 * A029652 A129510 A087913
Adjacent sequences: A002969 A002970 A002971 * A002973 A002974 A002975
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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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