|
|
A091155
|
|
Numbers n such that n - 2^k is squarefree for all 1 <= 2^k < n.
|
|
1
|
|
|
2, 3, 4, 7, 15, 23, 39, 63, 75, 87, 111, 135, 147, 159, 195, 219, 231, 255, 267, 315, 387, 399, 411, 423, 435, 447, 459, 495, 519, 567, 615, 663, 675, 699, 711, 735, 747, 759, 771, 819, 867, 915, 999, 1011, 1023, 1035, 1047, 1071, 1095, 1119, 1155, 1167, 1263
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
Cf. A039669 (n such that n-2^k are all primes).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|