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Semiprimes of the form (2^k - m)*(m*2^k - 1).
2

%I #28 Mar 14 2014 11:33:22

%S 9,14,49,55,94,115,446,611,869,961,4031,4315,7891,7934,8143,11651,

%T 16129,16255,32254,37301,51089,54701,60311,64931,65279,65441,241519,

%U 287509,321029,367459,384799,446201,495409,513847,521029,808691,1297915,1582619,1685219,1883681

%N Semiprimes of the form (2^k - m)*(m*2^k - 1).

%H Charles R Greathouse IV, <a href="/A239038/b239038.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 is in this sequence because (2^1-1)*(1*2^1-1) = 3*3 = 9 is semiprime for k=1 and m=1,

%e 49 is in this sequence because (2^3-1)*(1*2^3-1) = 7*7 = 49 is semiprime for k=3 and m=1,

%e 115 is in this sequence because (2^3-3)*(3*2^3-1) = 5*23 = 115 is semiprime for k=3 and m=3.

%o (PARI) list(lim)=my(v=List(),t); for(k=1,log(sqrt(lim)+2)\log(2), for(m=1, min((lim+1)>>k,2^k-2),my(a=2^k-m,b=m<<k-1,n=a*b); if(n<=lim && isprime(a) && isprime(b), listput(v,n))); t=4^k-2^k-1; if(t<=lim && bigomega(t)==2,listput(v, t))); Set(v) \\ _Charles R Greathouse IV_, Mar 11 2014

%Y Cf. A000668 (Mersenne primes).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Mar 09 2014

%E Missing terms inserted by _Charles R Greathouse IV_, Mar 11 2014