A166320 Numbers which are proper divisors of the number obtained by cyclic right-shift by 2 positions.

142857, 153846, 190476, 230769, 238095, 307692, 142857142857, 153846153846, 190476190476, 230769230769, 238095238095, 307692307692, 1176470588235294, 100250626566416040, 102756892230576441, 105263157894736842, 107769423558897243

Offset

1,1

Comments

Numbers which are invariant under the cyclic shift are not in the sequence, because they are not proper divisors of themselves.

Links

Table of n, a(n) for n=1..17.

Example

153846 is a proper divisor of 461538, obtained by moving the two least significant digits "46" to the front.
230769 is a proper divisor of 692307, obtained by moving the least significant digits "69" to the front.

Maple

cycShft := proc(n) local L, Ls ; if n < 100 then n; else L := convert(n, base, 10) ; Ls := [op(3..nops(L), L), op(1..2, L)] ; add(op(i, Ls)*10^(i-1), i=1..nops(Ls)) ; end if; end proc:
isA166320 := proc(n) local c; c := cycShft(n) ; return c mod n = 0 and c <> n ; end:
for n from 100 do if isA166320(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Oct 14 2009

Prog

(PARI) { genupto(m) = R = []; for(k=2, 9, for(a=10*k, 99, d = 100*k - 1; q = znorder( Mod(10, d/gcd(d, a)) ); forstep(z=q, m, q, R = concat(R, [(10^z-1)*a/d]); ); ); ); vecsort(R, , 8) } \\ generate all terms of length up to m. Max Alekseyev, Jan 22 2012

Crossrefs

Sequence in context: A086999 A175694 A023089 * A101202 A323711 A306265

Adjacent sequences: A166317 A166318 A166319 * A166321 A166322 A166323

Keyword

nonn,base

Author

Claudio Meller, Oct 11 2009

Extensions

keyword:base added by R. J. Mathar, Oct 14 2009

Corrected my number typo in the examples - R. J. Mathar, Oct 23 2009

More terms from Sean A. Irvine, Feb 25 2010

More terms from Max Alekseyev, Jan 22 2012

Status

approved