login
A179383
a(n) = 2*k(n)-1 where k(n) is the sequence of positions of records inA179382.
7
1, 5, 9, 11, 13, 19, 25, 29, 37, 53, 59, 61, 67, 83, 101, 107, 121, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757
OFFSET
1,2
COMMENTS
Records inA179382(k(n)) = 1, 2, 3, 5, 6, 9, 10, 14, 18, 26, 29,....
are located at k(n) = 1, 3, 5, 6, 7, 10, 13, 15, 19, 27, 30, 31,..
The current sequence is a simple transformation of this k(n) sequence.
Question: Are there any terms in the sequence with two or more distinct prime divisors?
Some very plausible conjectures: 1) The sequence consists of primes and squares of primes; 2) The set of squares is finite; 3) A prime p>=5 is in the sequence iff it has primitive root 2 (A001122); 4) There exists l such that, for n>l,A179383(n) =A139099(n+l). [FromVladimir Shevelev,Jul 14 2010]
LINKS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev,Jul 12 2010
EXTENSIONS
Definition rephrased and sequence extended byR. J. Mathar,Jul 13 2010
I made a change to Conjecture 4). -Vladimir Shevelev,Jul 18 2010
STATUS
approved