

A082130


2*n1 and 2*n+1 are semiprimes.


4



17, 25, 28, 43, 46, 47, 60, 61, 71, 72, 80, 92, 93, 101, 102, 107, 108, 109, 110, 118, 124, 133, 144, 145, 150, 151, 152, 160, 161, 164, 170, 196, 197, 206, 207, 208, 223, 226, 235, 236, 258, 259, 264, 267, 268, 272, 276, 290, 291, 295
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OFFSET

1,1


COMMENTS

Let p and q be distinct odd primes, and take a and b so that a*p  b*q = 1. Dickson's conjecture implies there are infinitely many k such that 2*a+k*q and 2*b+k*p are prime, in which case n = a*p + (k*q*p1)/2 is in the sequence with 2*n1 = (2*b+k*p)*q and 2*n+1 = (2*a+k*q)*p.  Robert Israel, Aug 13 2018


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Dickson's conjecture


EXAMPLE

a(1)=17 because 2*171=33=3*11 and 2*17+1=35=5*7 are both semiprimes.


MAPLE

OSP:= select(numtheory:bigomega=2, {seq(i, i=3..1000, 2)}):
R:= map(t > (t+1)/2, OSP intersect map(``, OSP, 2)):
sort(convert(R, list)); # Robert Israel, Aug 13 2018


PROG

(PARI) isok(n) = (bigomega(2*n1) == 2) && (bigomega(2*n+1) == 2); \\ Michel Marcus, Jul 16 2017


CROSSREFS

Cf. A001358, A082131.
Sequence in context: A272635 A105448 A336007 * A140609 A131275 A227238
Adjacent sequences: A082127 A082128 A082129 * A082131 A082132 A082133


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Apr 04 2003


EXTENSIONS

More terms from Jud McCranie, Apr 04 2003


STATUS

approved



