OFFSET
1,2
COMMENTS
Numbers that are not a sum of distinct Mersenne exponents (A000043). - Vladeta Jovovic, Jan 01 2003
Because there is a large gap between the 31st and 32nd Mersenne exponents, all k between 704338 and 756839 are in this sequence. - T. D. Noe, Oct 12 2006
Using all known Mersenne exponents, there are exactly 52935 terms in this sequence. When a new Mersenne prime (with exponent q) is found, there will be no new terms if the sum of the previous Mersenne exponents (A109472) is greater than q - 22.
REFERENCES
S. Kravitz, "Beware of the Fifth", Solution to Problem 2309, Journal of Recreational Mathematics, 29(1):76 Baywood NY 1998.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..300
EXAMPLE
a(2)=4 because no positive integer value of x can satisfy sigma(x) = 2^4 = 16.
MATHEMATICA
e={2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269}; u={0}; Do[u=Union[u, u+e[[k]]], {k, Length[e]}]; Complement[Range[e[[-1]]], u]
CROSSREFS
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Dec 29 2002
EXTENSIONS
More terms from Vladeta Jovovic, Jan 01 2003
Edited by N. J. A. Sloane, Aug 23 2010
Edited by Max Alekseyev, Jan 24 2014
STATUS
approved