Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #30 Aug 11 2024 14:41:34
%S 1,2,3,4,5,6,7,8,9,27,37,101,202,303,404,505,606,707,808,909,1084,
%T 1355,1626,1897,2168,2439,10101,10582,10989,11583,11655,12987,13986,
%U 15444,15873,16317,18648,19305,20202,20979,21164,23166,25641,26455,27027,30303,30888
%N 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 For palindromic numbers the ratio is equal to 10.
%H 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 P. De Geest, <a href="https://www.worldofnumbers.com/em174.htm">Hopping Numerals</a>
%e 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 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 P:=proc(q) local a,n; for n from 1 to q do
%p a:=(n mod 10)*10^(ilog10(n)+1)+trunc(n/10);
%p if not a=n then if type(a/n,integer) then print(n);
%p fi; fi; od; end: P(10^7);
%t Select[Range@31000,IntegerQ[FromDigits[RotateRight[Insert[IntegerDigits[#],0,1]]]/#]&] (* _Ivan N. Ianakiev_, May 28 2015 *)
%o (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 Cf. A034089.
%K nonn,base
%O 1,2
%A _Paolo P. Lava_, May 06 2015
%E 'Name' and 'Examples' sections reworded by _Ivan N. Ianakiev_, Aug 05 2015 (following the suggestion of _Jon E. Schoenfield_)