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 A098592 #38 Jan 06 2025 22:28:50 %S A098592 10,7,7,6,5,6,5,6,5,5,4,6,5,4,6,5,5,2,5,5,5,6,4,4,4,5,3,6,4,4,4,4,4,5, %T A098592 5,4,6,3,3,4,5,4,4,6,2,3,3,5,4,7,2,5,4,6,3,4,4,3,4,4,3,2,7,3,3,3,5,5, %U A098592 3,5,3,5,2,3,4,4,5,3,4,7,3,4,3,1,5,3,3,3,4,7,5,4,3,5,3,4,4,3,4,2,4,3,5,2,2,3 %N A098592 Number of primes between n*30 and (n+1)*30. %C A098592 Number of nonzero bits in A098591(n). %C A098592 The number a(n) is < 8 except for n=0. - _Pierre CAMI_, Jun 02 2009 %C A098592 For references to positions where a(n) = 7 and related explanation, see A100418. - _Peter Munn_, Sep 06 2023 %H A098592 Dennis Martin, <a href="/A005867/a005867.pdf">Proofs Regarding Primorial Patterns</a> [Cached copy, with permission of the author]. %H A098592 Hugo Pfoertner, <a href="http://www.randomwalk.de/scimath/primes30.pdf">Patterns count table</a>. %e A098592 a(1)=7 because there are 7 primes in the interval (30,60): 31,37,41,43,47,53,59. %e A098592 a(26)=3 because the interval of length 30 following 26*30=780 contains 3 primes: 787, 797 and 809. %o A098592 (FORTRAN) ! See links given in A098591. %o A098592 (PARI) a(n) = primepi(30*(n+1)) - primepi(30*n); \\ _Michel Marcus_, Apr 04 2020 %o A098592 (Python) %o A098592 from sympy import primerange %o A098592 def a(n): return len(list(primerange(n*30, (n+1)*30))) %o A098592 print([a(n) for n in range(106)]) # _Michael S. Branicky_, Oct 07 2021 %Y A098592 Cf. A000040 (prime numbers), A098591 (packed representation of the primes mod 30), A100418, A185641. %Y A098592 Cf. A038822, A094892. %K A098592 easy,nonn %O A098592 0,1 %A A098592 _Hugo Pfoertner_, Sep 16 2004 %E A098592 Edited by _N. J. A. Sloane_, Jun 12 2009 at the suggestion of _R. J. Mathar_