## 19404Prime Chain of 147

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• Jun 4, 2008
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This is a Prime Chain of 147 terms consisting of the output of
four equations that alternate sequentially.The equations are
either subsequences of x^2 - 79x + 1601 or transforms.
The four equations are :
4x^2 -146x +1373, 4x^2 -144x + 1459,
4x^2 -142x + 1301, 4x^2 -140x + 1877

1373,1459,1301,1877,1231,1319,1163,1741,1097,1187,1033,1613...

This Pascal Procedure can probably be imported into Borland's
latest programming software and run without any changes.

procedure Ndegrees3;
var a : array[0..16] of extended;
ct: longint;
n,nh ,i,j : integer;
ab1,ab2 : extended;
begin
for i := 0 to 16 do
a[i] := 0;
N := 5;
a[0] := 1373{ FIRST TERM OF PRIME CHAIN};
writeln('1');
writeln(trunc(a[0]));
writeln;
nh := 1;
a[1] := 1459 ;a[2] := 1301 ;a[3] := 1877 ;
a[4] := 1231 ;a[5] := 1319 ;

repeat
for i := N downto nh do
begin
a[i] := a[i] - a[i-1] ;
IF NH = 3 THEN A[I] := ABS(A[I]); {******}
End;
nh := nh + 1;
until nh = n + 2;
ct := 0;
repeat
ct := ct + 1;
ab1 := a[n] + a[n-1];
for i := N-1 downto 1 do
begin
ab2 := a[i] + a[i-1] ;
a[i] := ab1;
ab1 := ab2;
end;
IF ODD(ct + 1) THEN A[5] := -A[5];{******}
A[3] := -A[3];{******}
a[0] := ab1;
writeln(ct + 1);
writeln(trunc(a[0]));{}