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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 (list; graph; refs; listen; history; text; internal format)
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
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

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Last modified May 22 19:48 EDT 2024. Contains 372758 sequences. (Running on oeis4.)