cp's OEIS Frontend

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.

%I A256005 #30 Aug 11 2024 14:41:34
%S A256005 1,2,3,4,5,6,7,8,9,27,37,101,202,303,404,505,606,707,808,909,1084,
%T A256005 1355,1626,1897,2168,2439,10101,10582,10989,11583,11655,12987,13986,
%U A256005 15444,15873,16317,18648,19305,20202,20979,21164,23166,25641,26455,27027,30303,30888
%N 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.
%C A256005 For palindromic numbers the ratio is equal to 10.
%H A256005 Paolo P. Lava and Giovanni Resta, <a href="/A256005/b256005.txt">Table of n, a(n) for n = 1..504</a> (terms < 10^34, first 100 terms from Paolo P. Lava)
%H A256005 P. De Geest, <a href="https://www.worldofnumbers.com/em174.htm">Hopping Numerals</a>
%e A256005 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.
%e A256005 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.
%p A256005 P:=proc(q) local a,n; for n from 1 to q do
%p A256005 a:=(n mod 10)*10^(ilog10(n)+1)+trunc(n/10);
%p A256005 if not a=n then if type(a/n,integer) then print(n);
%p A256005 fi; fi; od; end: P(10^7);
%t A256005 Select[Range@31000,IntegerQ[FromDigits[RotateRight[Insert[IntegerDigits[#],0,1]]]/#]&] (* _Ivan N. Ianakiev_, May 28 2015 *)
%o A256005 (PARI) is(n)=my(k=n%10*10^#digits(n)+n\10); k>n && k%n==0 \\ _Charles R Greathouse IV_, May 08 2015
%Y A256005 Cf. A034089.
%K A256005 nonn,base
%O A256005 1,2
%A A256005 _Paolo P. Lava_, May 06 2015
%E A256005 'Name' and 'Examples' sections reworded by _Ivan N. Ianakiev_, Aug 05 2015 (following the suggestion of _Jon E. Schoenfield_)