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A140125
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
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
OFFSET
1,1
COMMENTS
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.
FORMULA
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.
PROG
(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;
CROSSREFS
Sequence in context: A155925 A329917 A060981 * A179915 A168167 A069490
KEYWORD
nonn,fini,full,uned
AUTHOR
Aldrich Stevens (aldrichstevens(AT)msn.com), Jun 04 2008
EXTENSIONS
Edited by Charles R Greathouse IV, Nov 03 2009
More terms from Jinyuan Wang, Jun 20 2021
STATUS
approved