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Ambitious numbers: numbers n with the property that if a number ends in n then it is divisible by n.
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%I #21 Sep 17 2024 23:36:33

%S 1,2,5,10,20,25,50,100,125,200,250,500,1000,1250,2000,2500,5000,10000,

%T 12500,20000,25000,50000,100000,125000,200000,250000,500000,1000000,

%U 1250000,2000000,2500000,5000000,10000000,12500000,20000000,25000000

%N Ambitious numbers: numbers n with the property that if a number ends in n then it is divisible by n.

%C Number whose 10's complement (A089186) is a multiple of it. 125 is a member as its 10's complement is 1000-125 = 875 = 125*7. - _Amarnath Murthy_, Mar 08 2002

%D P. J. Davis and R. Hersh, The Mathematical Experience, Birkhäuser, Boston and Basel, 1981; see pp. 293-298.

%H Problem of the week, <a href="http://mathforum.org/wagon">Web site</a> - problem 881

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,10).

%F Consists of the numbers 1, 2, 5, 25 or 125 times a power of 10.

%F a(n) = 10*a(n-5). - _Wesley Ivan Hurt_, May 03 2023

%e If a number ends in 2 then it is even and so is divisible by 2, so 2 is in the sequence.

%t LinearRecurrence[{0,0,0,0,10},{1,2,5,10,20,25,50,100,125},40] (* _Harvey P. Dale_, Sep 08 2018 *)

%Y Cf. A039690, A089186.

%K nonn,base,easy

%O 1,2

%A _Erich Friedman_

%E Entry revised by _N. J. A. Sloane_, Aug 03 2004