cp's OEIS Frontend

A247200 Odd numbers which are neither of the form p*2^m + 1 nor of the form p*2^m - 1 with p prime.

%I A247200 #33 Sep 08 2022 08:46:09
%S A247200 71,99,101,109,131,139,155,169,181,197,199,221,229,239,241,251,259,
%T A247200 265,281,287,289,307,309,311,323,337,339,341,349,365,371,373,379,391,
%U A247200 401,407,409,419,431,433,439,441,443,461,469,475,485,491,493,499,505,517,519
%N A247200 Odd numbers which are neither of the form p*2^m + 1 nor of the form p*2^m - 1 with p prime.
%C A247200 For each n, the sequence has a set of n consecutive odd numbers.
%C A247200 For any n, the number 2*A140077(n) + 1 is in the sequence.
%C A247200 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.
%C A247200 Odd numbers n such that (n-1)/A007814(n-1) and (n+1)/A007814(n+1) are composite. - _Robert Israel_, Nov 19 2014
%p A247200 filter:= proc(n)
%p A247200   local m1,m2;
%p A247200   m1:= padic[ordp](n-1,2);
%p A247200   if n-1 = 2^m1 then return false fi;
%p A247200   m2:= padic[ordp](n+1,2);
%p A247200   n+1 <> 2^m2 and not isprime((n-1)/2^m1) and not isprime((n+1)/2^m2);
%p A247200 end proc:
%p A247200 select(filter, [seq(2*i+1,i=0..1000)]); # _Robert Israel_, Nov 19 2014
%o A247200 (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;
%o A247200 (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, ", ")));
%Y A247200 Cf. A007814, A140077.
%K A247200 nonn
%O A247200 1,1
%A A247200 _Arkadiusz Wesolowski_, Nov 18 2014