A101983 Numbers that do not occur in A101909 (= number of primes between 2n and 4n).

11, 79, 134, 184, 186, 215, 245, 262, 284, 305, 387, 544, 694, 700, 706, 776, 814, 881, 939, 974, 1002, 1027, 1079, 1104, 1133, 1146, 1184, 1193, 1207, 1354, 1387, 1415, 1441, 1495, 1574, 1587, 1608, 1662, 1690, 1801, 1915, 1987, 2054, 2067, 2104, 2170

Offset: 1

Author

Cino Hilliard, Jan 28 2005

Keywords

• easy
• nonn

Examples

			11 is the first number that does not equal a count of primes between 2n and 4n for some n.
		

Crossrefs

Complement of A101947.

Cf. A101909.

Programs

Mathematica

f[n_] := PrimePi[4n] - PrimePi[2n]; t = Union[ Table[ f[n], {n, 12000}]]; Complement[ Range[ t[[ -1]]], t] (* Robert G. Wilson v, Feb 10 2005 *)

PARI

bet2n4n(n)={ my( b=vecsort(vector(n, x, my(c=0); forprime(y=2*x+1,4*x-1, c++); c))); for(x=1,n-2, while(b[x+1]-b[x]>1,print1(b[x]++,",")))} \\ It's probably faster to use A101909 instead of forprime(...). Edited and corrected by M. F. Hasler, Sep 29 2019

PARI

primecount(a,b)=primepi(b)-primepi(a);
v=vector(20000);
for(k=1,oo,j=primecount(2*k,4*k);if(j>#v,break,v[j]++));
for(k=1,2170,if(v[k]==0,print1(k,", "))) \\ Hugo Pfoertner, Sep 29 2019

Extensions

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

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