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 A342071 #6 Mar 23 2021 21:32:23 %S A342071 12,19,22,32,42,45,49,50,52,54,57,59,70,71,72,73,74,75,101,102,115, %T A342071 116,117,121,122,123,124,126,132,143,180,182,184,185,186,187,188,189, %U A342071 190,192,194,195,197,268,269,309,310,311,312,322,323,325,326,327,328,329 %N A342071 Numbers k such that there are more primes in the interval [3*k+1, 4*k] than there are in the interval [2*k+1, 3*k]. %C A342071 After a(194)=3977, there are no more terms < 100000. %C A342071 Conjecture: a(194)=3977 is the final term. %C A342071 For each of the first 194 terms k, there are at least as many primes in [1, k] as there are in [k+1, 2*k], and at least as many primes in [k+1, 2*k] as there are in [2*k+1, 3*k], so A342068(k)=4. %e A342071 The intervals [1, 100], [101, 200], [201, 300], and [301, 400] contain 25, 21, 16, and 16 primes respectively (cf. A038822); the 4th interval does not contain more primes than does the 3rd, so 100 is not a term of the sequence. %e A342071 However, the intervals [1, 101], [102, 202], [203, 303], and [304, 404] contain 26, 20, 16, and 17 primes, respectively; 17 > 16, so 101 is a term. %Y A342071 Cf. A342068, A342069, A342070, A342839. %K A342071 nonn %O A342071 1,1 %A A342071 _Jon E. Schoenfield_, Mar 23 2021