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 A002972 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) 16
 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; text; internal format)
 OFFSET 1,2 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)). [Reinhard Zumkeller, 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] (a(n)-1)/2 = A208295(n), n>=1. [Wolfdieter Lang, Mar 03 2012] a(A267858(k)) == 1 (mod 4), k >= 1. - Wolfdieter Lang, Feb 18 2016 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). LINKS T. D. Noe, Table of n, a(n) for n=1..1000 S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007. E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, Gordon and Breach, NY, 1971. [Annotated scans of a few pages] FORMULA a(n) = MIN(A173330(n), A002144(n) - A173330(n)). [Reinhard Zumkeller, Feb 16 2010] EXAMPLE The 2nd prime of the form 4i+1 is 13=2^2+3^2, so a(2)=3. MATHEMATICA pmax = 1000; odd[p_] := Module[{k, m}, 2m+1 /. ToRules[Reduce[k>0 && m >= 0 && (2k)^2 + (2m+1)^2 == p, {k, m}, Integers]]]; For[n=1; p=5, p

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)