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

71, 99, 101, 109, 131, 139, 155, 169, 181, 197, 199, 221, 229, 239, 241, 251, 259, 265, 281, 287, 289, 307, 309, 311, 323, 337, 339, 341, 349, 365, 371, 373, 379, 391, 401, 407, 409, 419, 431, 433, 439, 441, 443, 461, 469, 475, 485, 491, 493, 499, 505, 517, 519

Offset: 1

Author

Arkadiusz Wesolowski, Nov 18 2014

Keywords

• nonn

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

Crossrefs

Cf. A007814, A140077.

Programs

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;

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

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, ", ")));