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, 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

Offset

1,2

Comments

For palindromic numbers the ratio is equal to 10.

Links

Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 1..504 (terms < 10^34, first 100 terms from Paolo P. Lava)

P. De Geest, Hopping Numerals

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

(PARI) is(n)=my(k=n%10*10^#digits(n)+n\10); k>n && k%n==0 \\ Charles R Greathouse IV, May 08 2015

Crossrefs

Cf. A034089.

Sequence in context: A179988 A364187 A179979 * A031309 A122621 A229547

Adjacent sequences: A256002 A256003 A256004 * A256006 A256007 A256008

Keyword

nonn,base

Author

Paolo P. Lava, May 06 2015

Extensions

'Name' and 'Examples' sections reworded by Ivan N. Ianakiev, Aug 05 2015 (following the suggestion of Jon E. Schoenfield)

Status

approved