

A002972


a(n) is the odd member of {x,y}, where x^2 + y^2 is the nth 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
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OFFSET

1,2


COMMENTS

It appears that the terms in this sequence are the absolute values of the terms in A046730.  Gerry Myerson, Dec 02 2010


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



FORMULA



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<pmax, p = NextPrime[p], If[Mod[p, 4] == 1, a[n] = odd[p]; Print["a(", n, ") = ", a[n]]; n++]]; Array[a, n1] (* JeanFrançois Alcover, Feb 26 2016 *)


PROG

(PARI) decomp2sq(p) = {my (m=(p1)/4, r, x, limit=ceil(sqrt(p))); if (p>4 && denominator(m)==1, forprime (c=2, oo, if (!issquare(Mod(c, p)), r=c; break)); x=lift (Mod(r, p)^m); until (p<limit, r=p%x; p=x; x=r); if(p^2+x^2==4*m+1, [p, x], [0, 0]), [0, 0])};
forprime (p=5, 1000, if (p%4==1, print1(select(x>x%2, decomp2sq(p))[1], ", "))) \\ Hugo Pfoertner, Aug 27 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



