OFFSET
1,2
COMMENTS
The sequence of "obstinate numbers", that is, odd numbers which cannot be written as prime + 2^i with i >= 0 is the same except for the initial 3. - N. J. A. Sloane, Apr 20 2008
The reference by Nathanson gives on page 206 a theorem of Erdos: There exists an infinite arithmetic progression of odd positive integers, none of which is of the form p+2^k.
Essentially the same as A006285. - R. J. Mathar, Jun 08 2008
REFERENCES
Nathanson, Melvyn B.; Additive Number Theory: The Classical Bases; Springer 1996
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 62.
LINKS
J. Z. Schroeder, Every Cubic Bipartite Graph has a Prime Labeling Except K_(3,3), Graphs and Combinatorics (2019) Vol. 35, No. 1, 119-140.
EXAMPLE
The integer 7 can be represented as 2^2 + 3, therefore it is not on this list. - Michael Taktikos, Feb 02 2009
a(2)=127 because none of the numbers 127-2, 127-4, 127-8, 127-16, 127-32, 127-64 is a prime.
MAPLE
(Maple program which returns -1 iff 2n+1 is obstinate, from N. J. A. Sloane, Apr 20 2008): f:=proc(n) local i, t1; t1:=2*n+1; i:=0; while 2^i < t1 do if isprime(t1-2^i) then RETURN(1); fi; i:=i+1; end do; RETURN(-1); end proc;
MATHEMATICA
s = {}; Do[Do[s = Union[s, {Prime[n] + 2^i}], {n, 2, 200}], {i, 1, 10}]; Print[Complement[Range[3, 1000, 2], s]]
zweier = Map[2^# &, Range[0, 30]]; primes = Table[Prime[i], {i, 1, 300}]; summen = Union[Flatten[ Table[zweier[[i]] + primes[[j]], {i, 1, 30}, {j, 1, 300}]]]; us = Select[summen, OddQ[ # ] &]; odds = Range[1, 1001, 2]; Complement[odds, us] (* Michael Taktikos, Feb 02 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David S. Newman, Sep 18 2007
EXTENSIONS
More terms and corrected definition from Stefan Steinerberger, Sep 24 2007
Edited by N. J. A. Sloane, Feb 12 2009 at the suggestion of R. J. Mathar
STATUS
approved