OFFSET
1,1
COMMENTS
Note that Bergerson's Alpha construction is applied to composite numbers only. Otherwise the sequence could not contain numbers which are twice a prime, like 30662 and 84662. - Giovanni Resta, Mar 11 2013
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, F31. Japanese edition, 1983. [The English edition is different.]
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..64
A. Ross Eckler, Howard Bergerson, Word Ways: 43:2 (2010), Article 2. [alternate link]
EXAMPLE
The number 87 is not in the sequence because it can be reached from 90 = 2*3*3*5, since 87 = 90-2-3-3+5. - Giovanni Resta, Mar 11 2013
MATHEMATICA
seq[n_] := Block[{T = 0*Range@n, f, m}, m[{p_, e_}] := p*Range[-e, e, 2]; Do[f = FactorInteger@z; If[Last/@f != {1}, T[[Select[z + Union[ Total /@ Tuples[m /@ f]], 0 < # <= n &]]] = 1], {z, 4, 2*n+4}]; Flatten@Position[T, 0]]; seq[10^5] (* Giovanni Resta, Mar 11 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Mar 23 2002
EXTENSIONS
Edited with three more terms based on the Ross Eckler article by Omar E. Pol, Sep 11 2010
a(10)-a(26) from Donovan Johnson, Oct 05 2010
STATUS
approved