OFFSET
1,1
COMMENTS
No more terms found up to p = 1277, 1277 being the first prime for which the complete factorization of 2^p-1 is not currently known (see GIMPS link). - Michel Marcus, Jan 20 2014
Conjecture: gpf(gpf(2^p-1)-1) = p for finitely many p.
Conjecture: gpf(lpf(2^p-1)-1) = p for infinitely many p.
Namely, for p = 2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, ... - Michael B. Porter, Jan 26 2014
Note that gpf(lpf(2^p-1)-1) = gpf(gpf(2^p-1)-1) = p for p = 2, 3, 5, 7, 11, 13, 29, 53. See DATA.
LINKS
EXAMPLE
For prime p=2, 2^p-1=3, gpf(3)=3, gpf(3-1)=2, so 2 is in the sequence.
For prime p=3, 2^p-1=7, gpf(7)=7, gpf(7-1)=3, so 3 is in the sequence.
MATHEMATICA
Select[Prime[Range[25]], FactorInteger[FactorInteger[2^# - 1][[-1, 1]] - 1][[-1, 1]] == # &] (* Alonso del Arte, Jan 19 2014 *)
PROG
(PARI) isok(p) = isprime(p) && (q = (vecmax(factor(2^p-1)[, 1]))) && (vecmax(factor(q-1)[, 1]) == p); \\ Michel Marcus, Jan 19 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Thomas Ordowski, Jan 19 2014
STATUS
approved