OFFSET
1,1
COMMENTS
D is unique iff x^2 - 1 is squarefree, in which case it follows with necessity that D=x^2-1 and y=1.
All terms are even. A014574 is a subsequence.
Conjecture: All terms of A002110 > 1 are a subsequence. - Griffin N. Macris, Apr 11 2016
All n such that n+1 and n-1 are in A056911. - Robert Israel, Apr 12 2016
The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^2) = 0.322634... (A065474). - Amiram Eldar, Feb 25 2021
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = 2*A272799(n). - Juri-Stepan Gerasimov, Jan 17 2017
MAPLE
select(t -> numtheory:-issqrfree(t^2-1), [seq(n, n=2..1000, 2)]); # Robert Israel, Apr 12 2016
MATHEMATICA
Select[Range[200], SquareFreeQ[#^2-1]&] (* Vladimir Joseph Stephan Orlovsky, Oct 26 2009 *)
PROG
(Magma) [n: n in [1..110] | IsSquarefree(n-1) and IsSquarefree(n+1)]; // Juri-Stepan Gerasimov, Jan 17 2017
(Python)
from itertools import count, islice
from sympy import factorint
def A067874_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda k:max(factorint(k-1).values(), default=1)==1 and max(factorint(k+1).values())==1, count(max(startvalue+(startvalue&1), 2), 2))
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Lekraj Beedassy, Feb 25 2002
EXTENSIONS
Corrected and extended by Max Alekseyev, Apr 26 2009
Further edited by Max Alekseyev, Apr 28 2009
STATUS
approved