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

1,1

Links

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

Formula

p=(q+r)/2, where q<p and r>p are two successive semiprimes closest to p.

Example

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.

Prog

(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

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.

Sequence in context: A045711 A090153 A188339 * A079385 A352690 A362252

Adjacent sequences: A103651 A103652 A103653 * A103655 A103656 A103657

Keyword

nonn

Author

Zak Seidov, Feb 12 2005

Status

approved