OFFSET
1,1
COMMENTS
The numbers k such that A332547(k) = 1 are given by A068194, a sequence of interest to Mersenne and Fermat, so this sequence may also be interesting.
The factors of the initial terms are 5, 2*3, 2^3, 11, 2^2*3, 23, 47, 2^5*3, 191, 2^6*3, 383, 2^8*3, 6143, 2^12*3, 786431, 2^18*3, ...
There are essentially two cases. Firstly n can be an odd prime and n+1 of the form 3*2^k. These are the terms of A007505 with 2 excluded. Otherwise n can be of the form 3*2^k and n+1 a prime. These are 1 less than the terms of A039687. In addition, 8 is a term which is a special case. - Andrew Howroyd, Feb 21 2020
PROG
(PARI) upto(n)={Set(concat([if(n<8, [], [8]), select(isprime, [3*2^k-1 |k<-[1..logint((n+1)\3, 2)]]), select(p->isprime(p+1), [3*2^k |k<-[1..logint(n\3, 2)]])]))} \\ Andrew Howroyd, Feb 21 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 21 2020
EXTENSIONS
Terms a(17) and beyond from Andrew Howroyd, Feb 21 2020
STATUS
approved