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A140125
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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.
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1
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1373, 1459, 1301, 1877, 1231, 1319, 1163, 1741, 1097, 1187, 1033, 1613, 971, 1063, 911, 1493, 853, 947, 797, 1381, 743, 839, 691, 1277, 641, 739, 593, 1181, 547, 647, 503, 1093, 461, 563, 421, 1013, 383, 487, 347, 941, 313, 419, 281, 877, 251, 359, 223, 821, 197
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OFFSET
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1,1
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COMMENTS
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It may be possible to generate prime chains of any arbitrary length using minor variations of the procedure below.
This sequence consists of 147 primes, of which 74 are distinct and 73 are duplicates of earlier terms.
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LINKS
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FORMULA
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a(4n+1) = 4*n^2 - 146*n + 1373,
a(4n+2) = 4*n^2 - 144*n + 1459,
a(4n+3) = 4*n^2 - 142*n + 1301,
a(4n+4) = 4*n^2 - 140*n + 1877.
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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn,fini,full,uned
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AUTHOR
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Aldrich Stevens (aldrichstevens(AT)msn.com), Jun 04 2008
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EXTENSIONS
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STATUS
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approved
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