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 A342070 #11 Mar 24 2021 08:48:18 %S A342070 5,8,14,18,20,29,47,48,67,68,81,95,109,110,111,113,168,173,277,278, %T A342070 280,281,283,284,288,293,295,296,710,711,713,1323 %N A342070 Numbers k such that there are more primes in the interval [2*k+1, 3*k] than there are in the interval [k+1, 2*k]. %C A342070 Conjecture: 1323 is the final term. %C A342070 If there are at least as many primes in [1, m] as there are in [m+1, 2*m] for all positive integers m, then this sequence consists of the numbers k such that A342068(k)=3. %e A342070 The intervals [1, 100], [101, 200], and [201, 300] contain 25, 21, and 16 primes respectively (cf. A038822); 16 < 21, so 100 is not a term of the sequence. %e A342070 The intervals [1, 20], [21, 40], and [41, 60] contain 8, 4, and 5 primes, respectively; 5 > 4, so 20 is a term. %o A342070 (Python) %o A342070 from sympy import primepi %o A342070 def ok(n): return primepi(3*n) > 2*primepi(2*n) - primepi(n) %o A342070 print([m for m in range(9999) if ok(m)]) # _Michael S. Branicky_, Mar 23 2021 %Y A342070 Cf. A038822, A342068, A342069, A342071, A342839. %K A342070 nonn,more %O A342070 1,1 %A A342070 _Jon E. Schoenfield_, Mar 23 2021