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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.
1

%I #22 Mar 28 2024 13:17:15

%S 1373,1459,1301,1877,1231,1319,1163,1741,1097,1187,1033,1613,971,1063,

%T 911,1493,853,947,797,1381,743,839,691,1277,641,739,593,1181,547,647,

%U 503,1093,461,563,421,1013,383,487,347,941,313,419,281,877,251,359,223,821,197

%N 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.

%C It may be possible to generate prime chains of any arbitrary length using minor variations of the procedure below.

%C This sequence consists of 147 primes, of which 74 are distinct and 73 are duplicates of earlier terms.

%H Jinyuan Wang, <a href="/A140125/b140125.txt">Table of n, a(n) for n = 1..147</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).

%F a(4n+1) = 4*n^2 - 146*n + 1373,

%F a(4n+2) = 4*n^2 - 144*n + 1459,

%F a(4n+3) = 4*n^2 - 142*n + 1301,

%F a(4n+4) = 4*n^2 - 140*n + 1877.

%o (Pascal) { This 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]));{} readln; until 1<0; END;

%K nonn,fini,full,uned

%O 1,1

%A Aldrich Stevens (aldrichstevens(AT)msn.com), Jun 04 2008

%E Edited by _Charles R Greathouse IV_, Nov 03 2009

%E More terms from _Jinyuan Wang_, Jun 20 2021