A239038 Semiprimes of the form (2^k - m)*(m*2^k - 1).

9, 14, 49, 55, 94, 115, 446, 611, 869, 961, 4031, 4315, 7891, 7934, 8143, 11651, 16129, 16255, 32254, 37301, 51089, 54701, 60311, 64931, 65279, 65441, 241519, 287509, 321029, 367459, 384799, 446201, 495409, 513847, 521029, 808691, 1297915, 1582619, 1685219, 1883681

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

9 is in this sequence because (2^1-1)*(1*2^1-1) = 3*3 = 9 is semiprime for k=1 and m=1,
49 is in this sequence because (2^3-1)*(1*2^3-1) = 7*7 = 49 is semiprime for k=3 and m=1,
115 is in this sequence because (2^3-3)*(3*2^3-1) = 5*23 = 115 is semiprime for k=3 and m=3.

Prog

(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

Crossrefs

Cf. A000668 (Mersenne primes).

Sequence in context: A294030 A079625 A027009 * A271596 A272275 A272051

Adjacent sequences: A239035 A239036 A239037 * A239039 A239040 A239041

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 09 2014

Extensions

Missing terms inserted by Charles R Greathouse IV, Mar 11 2014

Status

approved