

A256005


Numbers m such that the result of prepending a zero digit to m, removing the least significant digit D, and prepending D, is divisible by m.


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 27, 37, 101, 202, 303, 404, 505, 606, 707, 808, 909, 1084, 1355, 1626, 1897, 2168, 2439, 10101, 10582, 10989, 11583, 11655, 12987, 13986, 15444, 15873, 16317, 18648, 19305, 20202, 20979, 21164, 23166, 25641, 26455, 27027, 30303, 30888
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OFFSET

1,2


COMMENTS

For palindromic numbers the ratio is equal to 10.


LINKS



EXAMPLE

37 is in the sequence because prepending a 0 gives 037, removing the least significant digit 7 then gives 03, and finally prepending the 7 gives 703, which is divisible by 37.
25641 is in the sequence because prepending a 0 gives 025641, removing the least significant digit 1 then gives 025641, and finally prepending the 1 gives 102564, which is divisible by 25641.


MAPLE

P:=proc(q) local a, n; for n from 1 to q do
a:=(n mod 10)*10^(ilog10(n)+1)+trunc(n/10);
if not a=n then if type(a/n, integer) then print(n);
fi; fi; od; end: P(10^7);


MATHEMATICA

Select[Range@31000, IntegerQ[FromDigits[RotateRight[Insert[IntegerDigits[#], 0, 1]]]/#]&] (* Ivan N. Ianakiev, May 28 2015 *)


PROG



CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



