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 A386519 #15 Aug 04 2025 23:04:04 %S A386519 5,12,13,52,2431,16,153888,27417323062119920,223378173194137397198, %T A386519 452,406,150886,23,40,2153717,28,92971458509,130,40998 %N A386519 Index of the smallest prime p such that the number of digits L in the repeating decimal period of 1/p equals the n-th prime. %C A386519 In general, for (q,2*5)=1, the length of the period of 1/q is equal to the multiplicative order of 10 modulo q, which is the smallest k such that 10^k == 1 (mod q). It follows that a(n) must be a prime divisor of 10^prime(n)-1. Hence, apart from a(2), we have prime(a(n)) = A147555(n) and a(20) is the index of the prime 241573142393627673576957439049. - _Giovanni Resta_, Jul 24 2025 %e A386519 a(1) = 5, since the 5th prime, p = 11, has a repeating decimal period of length L = 2, and 2 = prime(1). There is no smaller prime for which the period length equals the 1st prime. %e A386519 n a(n) p L %e A386519 1 5 11 2 %e A386519 2 12 37 3 %e A386519 3 13 41 5 %e A386519 4 52 239 7 %e A386519 5 2431 21649 11 %e A386519 6 16 53 13 %e A386519 7 153888 2071723 17 %Y A386519 Cf. A072859, A002371, A249330, A147555. %K A386519 nonn,base,more,hard %O A386519 1,1 %A A386519 _Jean-Marc Rebert_, Jul 24 2025 %E A386519 a(8)-a(19) from _Giovanni Resta_, Jul 24 2025