
COMMENTS

Only four terms are known.
The first four Mersenne primes (p=2^q1 in A000668) are double Mersenne primes, i.e., in A103901. The next four yield a composite M(p) and therefore are in this sequence. The next larger Mersenne prime p = A000668(9) has already 19 digits and is much too large to enable us, as of today, to test the primality of 2^p1 (which would require over 10^8 gigabytes just to be stored in binary). This explains that only 4 terms are known of this sequence and of A103901; for all the 30+ remaining members of A000668 it is not known whether they belong to A103901 or to this sequence A103902.  M. F. Hasler, Jan 21 2015


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., SpringerVerlag, NY, 2004, Sec. A3.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, 1954, p. 16.
P. Ribenboim, The New Book of Prime Number Records, SpringerVerlag, NY, 1996, Chap. 2, Sec. VII.
