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A083970
Numbers n such that concatenation (reverse of n) and n is divisible by n.
2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 48, 50, 55, 60, 66, 70, 75, 77, 80, 88, 90, 99, 100, 101, 110, 111, 120, 121, 125, 131, 132, 141, 150, 151, 161, 165, 168, 171, 180, 181, 191, 198, 200, 202, 212, 220, 222, 225, 232
OFFSET
1,2
COMMENTS
From Sam Alexander, Oct 21 2003: (Start)
All palindromes (in decimal) occur in this sequence. If we can multiply a(k) by j without having to resort to any carrying over, then ja(k) is also in the sequence.
Saying that R(n) concat n is divisible by n is equivalent to saying that (10^d)R(n) is divisible by n, where d = the number of digits in n. (End)
Contains A008919. - Robert Israel, Jul 27 2015
LINKS
EXAMPLE
12 is a member as 2112 is divisible by 12 and 13 is not as 3113 is not divisible by 13.
MAPLE
filter:= proc(n) local L, m, i, v;
L:= convert(n, base, 10);
m:= nops(L);
v:= add(10^(2*m-i)*L[i], i=1..m);
evalb(v mod n = 0);
end proc:
select(filter, [$1..10000]); # Robert Israel, Jul 26 2015
MATHEMATICA
Select[ Range[ 250 ],
Divisible[
FromDigits[
Flatten[ { Reverse[ IntegerDigits[ # ] ] ,
IntegerDigits[ # ] } ] ], # ] & ]
(* Kevin Southwick, Jul 25 2015 *)
Select[Range[250], Divisible[IntegerReverse[#]*10^IntegerLength[#]+#, #]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 28 2020 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 21 2003
EXTENSIONS
Corrected and extended by Sam Alexander, Oct 21 2003
STATUS
approved