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A195190 Primes p such that there is only one prime number between semiprime(p) and semiprime(p+1). 2

%I #12 May 13 2013 01:54:20

%S 2,13,23,43,113,151,179,229,233,241,281,283,347,353,359,367,383,401,

%T 431,491,499,503,541,571,593,613,653,677,787,811,827,859,881,967,983,

%U 1051,1093,1117,1223,1237,1259,1277,1279,1289,1303,1409,1433,1453,1471,1493,1499,1511,1531,1549,1607

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

%H Charles R Greathouse IV, <a href="/A195190/b195190.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=2 because 2 is a prime and semiprime(2)=6<(only one prime 7)<9=semiprime(2+1),

%e a(2)=13 because 13 is a prime and semiprime(13)=35<(only one prime 37)<38=semiprime(13+1).

%o (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

%Y Gf. A001358.

%K nonn,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Sep 11 2011

%E Sequence corrected by _Charles R Greathouse IV_, Sep 11 2011

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)