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 A342839 #4 Mar 23 2021 21:32:33 %S A342839 1,4,7,9,10,15,16,22,23,24,25,34,36,37,39,40,47,55,56,57,58,64,67,82, %T A342839 84,86,87,88,91,93,94,95,96,97,98,99,100,102,104,105,106,107,130,133, %U A342839 134,135,136,137,138,139,140,141,142,144,146,147,148,149,150,153 %N A342839 Numbers k such that there are more primes in the interval [4*k+1, 5*k] than there are in the interval [3*k+1, 4*k]. %C A342839 After a(876) = 11895, there are no more terms < 100000. %C A342839 Conjecture: a(876) = 11895 is the final term. %C A342839 There exist eight terms k for which A342068(k) != 5: A342068(k) = 2 for k = 1; A342068(k) = 3 for k = 47, 67, 95, and 1323; and A342068(k)=4 for k = 22, 57, and 102. %e A342839 The intervals [1, 100], [101, 200], [201, 300], [301, 400], and [401, 500] contain 25, 21, 16, 16, and 17 primes, respectively (cf. A038822); 17 > 16, so 100 is a term of the sequence. %Y A342839 Cf. A342068, A342069, A342070, A342071. %K A342839 nonn %O A342839 1,2 %A A342839 _Jon E. Schoenfield_, Mar 23 2021