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A098592 Number of primes between n*30 and (n+1)*30. 1


%S 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 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 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 Number of primes between n*30 and (n+1)*30.

%C Number of nonzero bits in A098591(n).

%C The number a(n) is < 8 except for n=0. - _Pierre CAMI_, Jun 02 2009

%H Dennis Martin, <a href="/A005867/a005867.pdf">Proofs Regarding Primorial Patterns</a> [Cached copy, with permission of the author].

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/scimath/primes30.pdf">Patterns count table</a>.

%e a(1)=7 because there are 7 primes in the interval (30,60): 31,37,41,43,47,53,59.

%e a(26)=3 because the interval of length 30 following 26*30=780 contains 3 primes: 787, 797 and 809.

%o (FORTRAN) See links given in A098591.

%o (PARI) a(n) = primepi(30*(n+1)) - primepi(30*n); \\ _Michel Marcus_, Apr 04 2020

%Y Cf. A000040 (prime numbers), A098591 (packed representation of the primes mod 30), A185641.

%K nonn

%O 0,1

%A _Hugo Pfoertner_, Sep 16 2004

%E Edited by _N. J. A. Sloane_, Jun 12 2009 at the suggestion of _R. J. Mathar_

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)