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%I #11 Apr 14 2019 04:33:54
%S 1,31,29,-11,12,434,430,-60,48,1786,1750,-360,-152,4206,4194,-352,
%T -102,8284,8276,-378,60,13090,13054,-972,24,20798,20782,-816,72,28646,
%U 28630,-960,24,41402,41398,-576,60,54418,54382,-1980,24,69122,69118,-744,-1942,85944,85920,-2810,-896
%N Table which contains in row n the mapping of the n-th block of 4 primes to 4 integers.
%C The map takes 4 integers c, b, m and r and maps them onto four integers b*m-c*r, c*m+b*r, b*m+c*r and c*m-b*r, linked via (c^2+b^2)*(m^2+r^2) = (b*m-c*r)^2+(c*m+b*r)^2 = (b*m+c*r)^2+(c*m-b*r)^2.
%C Here, the inputs are four consecutive primes c=prime(4n-3), b=prime(4n-2), m=prime(4n-1) and r=prime(4n), and the four quadratic combinations which are the bases of the squares are placed into the n-th row of the table.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/DiophantineEquation2ndPowers.html">Diophantine Equation, 2nd powers</a>, MathWorld.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/FibonacciIdentity.html">Fibonacci identity</a>, MathWorld.
%F T(n,1) = prime(4*n-2)*prime(4*n-1) - prime(4*n-3)*prime(4*n).
%F T(n,2) = prime(4*n-3)*prime(4*n-1) + prime(4*n-2)*prime(4*n).
%F T(n,3) = prime(4*n-2)*prime(4*n-1) + prime(4*n-3)*prime(4*n).
%F T(n,4) = prime(4*n-3)*prime(4*n-1) - prime(4*n-2)*prime(4*n).
%e For n=3, the primes 23, 29, 31 and 37 are mixed via (23^2 + 29^2)*(31^2 + 37^2) = 48^2 + 1786^2 = 1750^2 + 360^2, and 48, 1786, 1750 and -360 from the right hand sides fill the third row of the table.
%p A162156 := proc(n,k) c := ithprime(4*n-3) ; b := nextprime(c) ; m := nextprime(b) ; r := nextprime(m) ; op(k, [b*m-c*r,c*m+b*r,b*m+c*r,c*m-b*r] ) ; end: seq(seq(A162156(n,k),k=1..4),n=1..20) ; # _R. J. Mathar_, Sep 16 2009
%Y Cf. A000040.
%K sign,tabf,less
%O 1,2
%A _Juri-Stepan Gerasimov_, Jun 26 2009
%E Edited and extended by _R. J. Mathar_, Sep 16 2009
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