A101984 -id:A101984 - 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

A101985 Numbers that occur exactly once in A289493 (= number of primes between 2n and 3n).

Original entry on oeis.org

11, 42, 93, 110, 113, 156, 186, 196, 197, 220, 252, 292, 298, 362, 403, 429, 493, 503, 609, 644, 659, 727, 735, 778, 790, 886, 888, 920, 932, 952, 953, 1008, 1023, 1024, 1079, 1093, 1094, 1100, 1109, 1136, 1165, 1208, 1212, 1213, 1226, 1238, 1250, 1311

Offset: 1

Cino Hilliard, Jan 29 2005

Cf. A289493, A101984.

f[n_] := PrimePi[3n] - PrimePi[2n]; t = Split[ Sort[ Table[ f[n], {n, 14000}] ]]; Flatten[ Select[t, Length[ # ] == 1 &]] (* Robert G. Wilson v, Feb 10 2005 *)

bet2n3n(n)={ my(b=vecsort( vector(n,x, my(c=0); forprime(y=2*x+1,3*x-1, c++); c))); for(x=1,n-2, if(b[x+1]>b[x] && b[x+1]A289493 and/or primepi(3n)-primepi(2n) would be faster. Edited and corrected by M. F. Hasler, Sep 29 2019

\\ Size of vector dependent on how pessimistic one is on smoothness of primepi
primecount(a, b)=primepi(b)-primepi(a);
v=vector(14000);
for(k=1, oo, j=primecount(2*k, 3*k); if(j>#v, break, v[j]++));
for(k=1, 1311, if(v[k]==1, print1(k, ", "))) \\ Hugo Pfoertner, Sep 29 2019

More terms from Robert G. Wilson v, Feb 10 2005

Name edited by M. F. Hasler, Sep 29 2019

cp's OEIS Frontend

A101909 Number of primes between 2n and 4n.

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A101985 Numbers that occur exactly once in A289493 (= number of primes between 2n and 3n).

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Author

Keywords

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Mathematica

PARI

PARI

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