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%I #13 Jun 24 2017 02:22:49
%S 142857,153846,190476,230769,238095,307692,142857142857,153846153846,
%T 190476190476,230769230769,238095238095,307692307692,1176470588235294,
%U 100250626566416040,102756892230576441,105263157894736842,107769423558897243
%N Numbers which are proper divisors of the number obtained by cyclic right-shift by 2 positions.
%C Numbers which are invariant under the cyclic shift are not in the sequence, because they are not proper divisors of themselves.
%e 153846 is a proper divisor of 461538, obtained by moving the two least significant digits "46" to the front.
%e 230769 is a proper divisor of 692307, obtained by moving the least significant digits "69" to the front.
%p 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:
%p isA166320 := proc(n) local c; c := cycShft(n) ; return c mod n = 0 and c <> n ; end:
%p for n from 100 do if isA166320(n) then printf("%d,\n",n) ; fi; od: # _R. J. Mathar_, Oct 14 2009
%o (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
%K nonn,base
%O 1,1
%A _Claudio Meller_, Oct 11 2009
%E keyword:base added by _R. J. Mathar_, Oct 14 2009
%E Corrected my number typo in the examples - _R. J. Mathar_, Oct 23 2009
%E More terms from _Sean A. Irvine_, Feb 25 2010
%E More terms from _Max Alekseyev_, Jan 22 2012
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