This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305531 #40 May 06 2021 23:10:27 %S A305531 1,1,1,2,1,1,2,1,3,10,3,1,2,1,1,4,1,29,14,1,1,14,2,1,2,4,1,2,4,5,12,2, %T A305531 1,2,2,9,16,1,2,80,1,2,4,2,3,16,2,2,2,1,15,960,15,1,4,3,1,14,1,6,20,1, %U A305531 3,946,6,1,18,10,1,4,1,5,42,4,1,828,1,1,2,1,12,2,6,4,30,3,3022,2,1,1 %N A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime. %C A305531 a(prime(j)) + 1 = A087139(j). %C A305531 a(123) > 10^5, a(342) > 10^5, see the Barnes link for the Sierpinski base-123 and base-342 problems. %C A305531 a(251) > 73000, see A087139. %H A305531 Eric Chen, <a href="/A305531/b305531.txt">Table of n, a(n) for n = 2..122</a> %H A305531 Gary Barnes, <a href="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm">Sierpinski conjectures and proofs</a> %H A305531 Eric Chen, <a href="/A305531/a305531.txt">Table n, a(n) for n = 2..360 status</a> %o A305531 (PARI) a(n)=for(k=1,2^16,if(ispseudoprime((n-1)*n^k+1),return(k))) %Y A305531 For the numbers k such that these forms are prime: %Y A305531 a1(b): numbers k such that (b-1)*b^k-1 is prime %Y A305531 a2(b): numbers k such that (b-1)*b^k+1 is prime %Y A305531 a3(b): numbers k such that (b+1)*b^k-1 is prime %Y A305531 a4(b): numbers k such that (b+1)*b^k+1 is prime (no such k exists when b == 1 (mod 3)) %Y A305531 a5(b): numbers k such that b^k-(b-1) is prime %Y A305531 a6(b): numbers k such that b^k+(b-1) is prime %Y A305531 a7(b): numbers k such that b^k-(b+1) is prime %Y A305531 a8(b): numbers k such that b^k+(b+1) is prime (no such k exists when b == 1 (mod 3)). %Y A305531 Using "-------" if there is currently no OEIS sequence and "xxxxxxx" if no such k exists (this occurs only for a4(b) and a8(b) for b == 1 (mod 3)): %Y A305531 . %Y A305531 b a1(b) a2(b) a3(b) a4(b) a5(b) a6(b) a7(b) a8(b) %Y A305531 -------------------------------------------------------------------- %Y A305531 2 A000043 ------- A002235 A002253 A000043 ------- A050414 A057732 %Y A305531 3 A003307 A003306 A005540 A005537 A014224 A051783 A058959 A058958 %Y A305531 4 A272057 ------- ------- xxxxxxx A059266 A089437 A217348 xxxxxxx %Y A305531 5 A046865 A204322 A257790 A143279 A059613 A124621 A165701 A089142 %Y A305531 6 A079906 A247260 ------- ------- A059614 A145106 A217352 A217351 %Y A305531 7 A046866 A245241 ------- xxxxxxx A191469 A217130 A217131 xxxxxxx %Y A305531 8 A268061 A269544 ------- ------- A217380 A217381 A217383 A217382 %Y A305531 9 A268356 A056799 ------- ------- A177093 A217385 A217493 A217492 %Y A305531 10 A056725 A056797 A111391 xxxxxxx A095714 A088275 A092767 xxxxxxx %Y A305531 11 A046867 A057462 ------- ------- ------- ------- ------- ------- %Y A305531 12 A079907 A251259 ------- ------- ------- A137654 ------- ------- %Y A305531 13 A297348 ------- ------- xxxxxxx ------- ------- ------- xxxxxxx %Y A305531 14 A273523 ------- ------- ------- ------- ------- ------- ------- %Y A305531 15 ------- ------- ------- ------- ------- ------- ------- ------- %Y A305531 16 ------- ------- ------- xxxxxxx ------- ------- ------- xxxxxxx %Y A305531 Cf. (smallest k such that these forms are prime) A122396 (a1(b)+1 for prime b), A087139 (a2(b)+1 for prime b), A113516 (a5(b)), A076845 (a6(b)), A178250 (a7(b)). %K A305531 nonn %O A305531 2,4 %A A305531 _Eric Chen_, Jun 04 2018