A195190 Primes p such that there is only one prime number between semiprime(p) and semiprime(p+1).

2, 13, 23, 43, 113, 151, 179, 229, 233, 241, 281, 283, 347, 353, 359, 367, 383, 401, 431, 491, 499, 503, 541, 571, 593, 613, 653, 677, 787, 811, 827, 859, 881, 967, 983, 1051, 1093, 1117, 1223, 1237, 1259, 1277, 1279, 1289, 1303, 1409, 1433, 1453, 1471, 1493, 1499, 1511, 1531, 1549, 1607

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 11 2011

Keywords

• nonn
• less

Examples

			a(1)=2 because 2 is a prime and semiprime(2)=6<(only one prime 7)<9=semiprime(2+1),
a(2)=13 because 13 is a prime and semiprime(13)=35<(only one prime 37)<38=semiprime(13+1).
		

Links

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

Crossrefs

Gf. A001358.

Programs

PARI

list(lim)=my(lm=1.1*lim*log(lim)/log(log(lim)),v=List(),u=List(),t);forprime(p=2, sqrt(lm), t=p;forprime(q=p, lm\t, listput(v,t*q))); v=vecsort(Vec(v)); forprime(p=2,lim,t=0;for(k=v[p]+1,v[p+1]-1,if(isprime(k)&&t++>1,break));if(t==1,listput(u,p))); v=0; Vec(u) \\ Charles R Greathouse IV, Sep 11 2011

Extensions

Sequence corrected by Charles R Greathouse IV, Sep 11 2011