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A068196
Origin numbers: integers unreachable by Bergerson's Alpha construction (see the Ross Eckler link).
1
28, 108, 6902, 16068, 30662, 84662, 117157, 175844, 305804, 636268, 760436, 765402, 1343537, 1433493, 2125253, 3125825, 3255917, 4264947, 4796654, 10271188, 11911557, 12043892, 15344303, 27692262, 28112662, 28478708
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
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
Sequence in context: A256647 A223492 A219857 * A044279 A044660 A183341
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