A103654 Primes which are the average of two successive semiprimes.

5, 53, 67, 89, 113, 131, 173, 211, 251, 293, 307, 337, 379, 409, 449, 487, 491, 499, 631, 683, 701, 727, 751, 769, 787, 919, 941, 953, 991, 1009, 1039, 1051, 1063, 1117, 1193, 1259, 1399, 1459, 1471, 1499, 1511, 1567, 1627, 1697, 1709, 1733, 1759, 1787, 1801

Offset: 1

Author

Zak Seidov, Feb 12 2005

Keywords

• nonn

Examples

			a(3)=67 because 65 and 69 are two successive semiprimes closest to 67 and 67=(65+69)/2;a(333)=22679 because 22677 and 22691 are two successive semiprimes closest to 22679 and 22679=(22677+22681)/2.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Indices of these primes: A103655. Primes: A000040, semiprimes: A001358, number of primes between successive semiprimes: A088700, number of semiprimes between two successive primes: A103668.

Cf. A000040, A088700, A103655, A001358, A103668, A103669.

Programs

PARI

list(lim)=my(v=List(),u=v,t,lim2=lim+log(lim)^2);forprime(p=2,sqrt(lim2),t=p;forprime(q=p,lim2\t,listput(v,t*q)));v=vecsort(Vec(v));for(i=2,#v,t=(v[i]+v[i-1])/2;if(denominator(t)==1&&isprime(t),if(t>lim,break,listput(u,t))));Vec(u) \\ Charles R Greathouse IV, Oct 08 2012

Formula

p=(q+r)/2, where q

p are two successive semiprimes closest to p.