OFFSET
1,1
COMMENTS
Erdos conjectures that this sequence is infinite. It appears that n = 3 (mod 12) except for n = 2, 4, 7 and 23.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A19.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
P. Erdõs, On integers of the form 2^k + p and some related problems, Summa Brasil. Math. 2 (1950), pp. 113-123.
EXAMPLE
39 is on the list because 38, 37, 35, 31, 23 and 7 are all squarefree.
MATHEMATICA
a={}; Do[k=1; While[sf=SquareFreeQ[n-k]; sf&&2k<n, k=2k]; If[sf, AppendTo[a, n]], {n, 2000}]; a
PROG
(PARI) is(n)=for(k=1, log(n+.5)\log(2), if(!issquarefree(n-2^k), return(0))); 1 \\ Charles R Greathouse IV, Apr 13 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Dec 23 2003
STATUS
approved