

A002973


a(n) is half of the even member of {x,y}, where x^2 + y^2 is the nth prime of the form 4i+1.
(Formerly M0135)


15



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
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OFFSET

1,3


COMMENTS



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 3rd prime of the form 4i+1 is 17 = 1^2 + 4^2, so a(3) = 4/2 = 2.


MATHEMATICA

pmax = 1000; k[p_] := Module[{k, m}, k /. 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] = k[p]; Print["a(", n, ") = ", a[n]]; n++]]; Array[a, n1] (* JeanFrançois Alcover, Feb 26 2016 *)


PROG

(PARI) \\ use function decomp2sq from A002972
forprime (p=5, 1000, if (p%4==1, print1(select(x>!(x%2), decomp2sq(p))[1]/2, ", "))) \\ Hugo Pfoertner, Aug 27 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



