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 - 79*x + 1601 or transforms. The four equations are 4*x^2 - 146*x + 1373, 4*x^2 - 144*x + 1459, 4*x^2 - 142*x + 1301, 4*x^2 - 140*x + 1877.

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

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

Links

Jinyuan Wang, Table of n, a(n) for n = 1..147

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

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.

a(n) = n^2/4 - 37*n + O(1). - Charles R Greathouse IV, Jun 03 2026

Mathematica

LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1373, 1459, 1301, 1877, 1231, 1319}, 50] (* Harvey P. Dale, Jun 17 2025 *)

Prog

(PARI) a(n)=(n^2-148*n+[8084, 5639, 6128, 5639][n%4+1])/4 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Sequence in context: A155925 A329917 A060981 * A179915 A168167 A069490

Adjacent sequences: A140122 A140123 A140124 * A140126 A140127 A140128

Keyword

nonn,fini,full,less,easy

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

Edited by Sean A. Irvine, Apr 08 2026

Status

approved