cp's OEIS Frontend

1, 2 and 5 are the only terms of this sequence which are also in A029544. - Gerasimov Sergey, Feb 23 2014

The next term with this property is > 10000. - Michael B. Porter, Feb 23 2014

The probability of a given number N being a twin prime grows like 1/(log(N))^2, so for a given n, the probability that it has this property is 1/n^2, and the sum converges. Are there any n for which n*2^n-1 and n*2^n+1 are both prime? - Michael B. Porter, Feb 25 2014

We can write (k+1)*2^k - 1 = {(k+1)/2}*4^{(k+1)/2} - 1, and when k is odd, this takes the form of a generalized Woodall prime (base 4). These are listed in A086661. In other words, {2*A086661 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019

The largest odd term currently known is 3986381 = 2*A086661(21) - 1. - Jeppe Stig Nielsen, Oct 16 2019

Generated by n = 1, 2, 3, 6, 7, 14, 27, 66, 67, 87, 115, .. = A029544(n)+1.

See also A236752 for primes of the form k*2^(k-1) - 1, and A230769 for the corresponding indices k (minus 1). - M. F. Hasler, Mar 01 2014

The fifth Fermat prime, 65537, is not in the sequence: 65537*2^65536-1 is composite (per PFGW). - Michael B. Porter, Feb 11 2014

Also 65537*2^65536-1 is divisible by 16267 and 2058772459. - Jeppe Stig Nielsen, Jan 04 2020