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A103654 Primes which are the average of two successive semiprimes. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A091272 A142399

Adjacent sequences:  A103651 A103652 A103653 * A103655 A103656 A103657

KEYWORD

nonn

AUTHOR

Zak Seidov, Feb 12 2005

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)