

A192544


Number bases n such that all integers m having the commuting property r(m)^2=r(m^2), where r is cyclic replacement of digits d>(d+1) mod n, are of the form m=A^kB, where B=n/2, A=B1, and 0<=k<=n3.


1



8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144
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OFFSET

1,1


COMMENTS

The number bases n form the arithmetic sequence n=8+4*k, k>=0, so B is necessarily even. The number bases n=2 and n=4 have B as the only number with the commuting property. No odd base n has the commuting property.


LINKS

Table of n, a(n) for n=1..35.


EXAMPLE

In base 8, B=4, A=3, and the numbers with the commuting property are 4, 34, 334, 3334, 33334, 333334.


CROSSREFS

Cf. A059558, A124354, A192544, A117755, A127856, A127857, A127859, A127860, A127861.
Sequence in context: A253296 A081925 A049199 * A302139 A160392 A242272
Adjacent sequences: A192541 A192542 A192543 * A192545 A192546 A192547


KEYWORD

nonn,base


AUTHOR

Walter Kehowski, Jul 04 2011


STATUS

approved



