A068196 Origin numbers: integers unreachable by Bergerson's Alpha construction (see the Ross Eckler link).

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

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

Sequence in context: A256647 A223492 A219857 * A044279 A044660 A183341

Adjacent sequences: A068193 A068194 A068195 * A068197 A068198 A068199

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