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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=B-1, and 0<=k<=n-3. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 16 14:50 EST 2018. Contains 318167 sequences. (Running on oeis4.)