1,1

This 196-term sequence may or may not break Euler's 250-year-old record of 80 for a quadratic chain of primes, depending on the interpretation of rules governing competitive comparisons.

Aldrich Stevens, Table of n, a(n) for n = 1..196

10a^2 + 19b^2, a = column 1:14, b = row 1:14, Take the value 'b' of each row and factor it. Remove all prime factors that are found in 'b' from its entire corresponding row (remove the 2'3 from row 2, the 3's from row 3...the 2'3,7's from row 14). Every remaining value is prime.

a = 13, b= 3, S(13,3) = 3229 (a prime)

a = 5, b= 5, S(5,5) = 725, 725/5 = 145. 145/5 = 29 (a prime)

a = 8, b= 14, S(7,14) = 4214, 4214/7 = 602, 602/7 = 86, 86/2 = 43 (a prime)

The array in full:

29 59 109 179 269 379 509 659 829 1019 1229 1459 1709 1979

86 116 166 236 326 436 566 716 886 1076 1286 1516 1766 2036

181 211 261 331 421 531 661 811 981 1171 1381 1611 1861 2131

314 344 394 464 554 664 794 944 1114 1304 1514 1744 1994 2264

485 515 565 635 725 835 965 1115 1285 1475 1685 1915 2165 2435

694 724 774 844 934 1044 1174 1324 1494 1684 1894 2124 2374 2644

941 971 1021 1091 1181 1291 1421 1571 1741 1931 2141 2731 2621 2891

1226 1256 1306 1376 1466 1576 1706 1856 2026 2216 2426 2656 2906 3176

1549 1579 1629 1699 1789 1899 2029 2179 2349 2539 2749 2979 3229 3499

1910 1940 1990 2060 2150 2260 2390 2540 2710 2900 3110 3340 3590 3860

2309 2339 2389 2459 2549 2669 2789 2939 3109 3299 3509 3739 3989 4259

2746 2776 2826 2896 2986 3096 3226 3376 3546 3736 3946 4176 4426 4696

3221 3251 3301 3371 3461 3571 3701 3851 4021 4211 4421 4651 4901 5171

3734 3764 3814 3884 3974 4084 4214 4364 4534 4724 4934 5164 5414 5684

Cf. A140340, A140755.

Sequence in context: A036062 A161928 A140340 this_sequence A047078 A042672 A042670

Adjacent sequences: A140751 A140752 A140753 this_sequence A140755 A140756 A140757

nonn,tabf,fini

Aldrich Stevens (aldrichstevens(AT)msn.com), May 27 2008

Edited with better definition by Omar E. Pol (info(AT)polprimos.com), Jan 05 2009