A101983 -id:A101983 - cp's OEIS frontend

A101909 Number of primes between 2n and 4n.

1, 2, 2, 2, 4, 4, 3, 5, 4, 4, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 9, 10, 9, 10, 12, 12, 13, 14, 13, 12, 13, 14, 13, 15, 14, 13, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 21, 20, 19, 20, 19, 18, 19, 19, 20, 21, 22, 23, 23, 24, 23, 24, 24, 24, 26, 25, 25, 27, 27, 27, 28, 27, 26

Offset: 1

Cino Hilliard, Jan 28 2005

T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A101947, A101983, A101984, A101985.

A101909 := proc(n::integer)
    numtheory[pi](4*n)-numtheory[pi](2*n) ;
end proc:
seq(A101909(n),n=1..100) ; # R. J. Mathar, Oct 02 2019

f[n_] := PrimePi[4n] - PrimePi[2n]; Table[ f[n], {n, 76}] (* Robert G. Wilson v, Feb 10 2005 *)

bet2n4n(n) = { local(c,x,y); forstep(x=2,n,2, c=0; forprime(y=x+1,x+x-1, c++; ); print1(c",") ) }

s=0;vector(100,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1)) \\ Charles R Greathouse IV, Mar 12 2012

a(n) = A099802(2*n)-A099802(n). - R. J. Mathar, Oct 02 2019

A101947 A101909 sorted and duplicates removed.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73

Offset: 1

Cino Hilliard, Jan 28 2005

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A101909, A101983-A101985.

bet2n4n(n) = { local(c,c1,x,y); a=vector(5001); for(x=1,n, c=0; forprime(y=2*x+1,4*x-1, c++; ); a[x] = c; ); b=vecsort(a); for(x=1,5000, if(b[x]>0, if(b[x]<>b[x+1],print1(b[x]",") ) ); ) }

s=0;v=vectorsmall(10^6,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1));v=vecsort(v,,8);vecextract(v,Str("1..",#v\2)) \\ Charles R Greathouse IV, Mar 12 2012

A101984 Numbers that occur exactly once in A101909 (= count of primes between 2n and 4n).

Original entry on oeis.org

1, 3, 5, 8, 22, 36, 37, 46, 47, 48, 53, 63, 83, 98, 99, 101, 105, 108, 113, 114, 127, 135, 139, 148, 150, 155, 158, 171, 172, 173, 174, 175, 177, 178, 188, 205, 210, 218, 219, 220, 221, 226, 231, 240, 246, 254, 277, 282, 297, 298, 301, 303, 327, 333, 334, 339

Offset: 1

Cino Hilliard, Jan 28 2005

			There are 5 primes between 16 and 32 and nowhere else between 2n and 4n.

Cf. A101909, A101947, A101983, A101985.

bet2n4n(n)={ my(b=vecsort(vector(n,x, my(c=0); forprime(y=2*x+1,4*x-1, c++); c))); print1(1","); for(x=1,n-2, if(b[x+1]>b[x] && b[x+1]Don Reble. - M. F. Hasler, Sep 29 2019

Better name from N. J. A. Sloane, Sep 29 2019

Corrected a(22) and a(45), following an observation by Don Reble. - M. F. Hasler, Sep 29 2019

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A101909 Number of primes between 2n and 4n.

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A101947 A101909 sorted and duplicates removed.

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A101984 Numbers that occur exactly once in A101909 (= count of primes between 2n and 4n).

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