OFFSET
1,1
COMMENTS
For each n, the sequence has a set of n consecutive odd numbers.
For any n, the number 2*A140077(n) + 1 is in the sequence.
Every number of the form S*2^n + 1 or R*2^n - 1 with n > 0, where S is a composite Sierpiński number and R is a composite Riesel number, is in the sequence.
Odd numbers n such that (n-1)/A007814(n-1) and (n+1)/A007814(n+1) are composite. - Robert Israel, Nov 19 2014
MAPLE
filter:= proc(n)
local m1, m2;
m1:= padic[ordp](n-1, 2);
if n-1 = 2^m1 then return false fi;
m2:= padic[ordp](n+1, 2);
n+1 <> 2^m2 and not isprime((n-1)/2^m1) and not isprime((n+1)/2^m2);
end proc:
select(filter, [seq(2*i+1, i=0..1000)]); # Robert Israel, Nov 19 2014
PROG
(Magma) lst1:=[]; lst2:=[]; r:=519; t:=Floor(Log(2, r))-1; for m in [0..t] do e:=Floor(r/2^m); for p in [2..e] do if IsPrime(p) then a:=p*2^m-1; b:=p*2^m+1; if not a in lst1 then Append(~lst1, a); end if; if not b in lst1 then Append(~lst1, b); end if; end if; end for; end for; for n in [3..r by 2] do if not n in lst1 then Append(~lst2, n); end if; end for; lst2;
(PARI) b=0; forstep(n=1, 519, 2, c=2^floor(log(n)/log(2)); a=b; b=(n+1)/gcd(n+1, c); if(a>8&&!isprime(a)&&!isprime(b), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Nov 18 2014
STATUS
approved