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

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

Author

Cino Hilliard, Jan 29 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A289493, A101984.

Programs

Mathematica

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 *)

PARI

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

PARI

\\ 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

Extensions

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

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