A177950 Numbers k that divide the digit reversal of k^2.
1, 2, 3, 9, 11, 22, 26, 33, 48, 66, 87, 99, 101, 111, 117, 121, 202, 212, 216, 264, 273, 288, 297, 307, 333, 484, 513, 528, 666, 783, 819, 836, 999, 1001, 1111, 1323, 1331, 1452, 1474, 1602, 2002, 2178, 2285, 2622, 2636, 3333, 4884, 4961, 6666, 7161, 7575
Offset: 1
Examples
273 is in the sequence because 273^2 = 74529 and 273|92547.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..171 (all terms up to k = 10 million)
Programs
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Maple
with(numtheory):T:=array(1..94):k:=1:for n from 1 to 200000 do: n0:=n^2:l:=length(n0) :s:=0:for m from l by -1 to 1 do:q:=n0:u:=irem(q,10):v:=iquo(q,10): n0:=v :s:=s+ u*10^(m-1):od:if irem(s,n)=0 then T[k]:=n:k:=k+1:else fi: od:print(T):
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Mathematica
Select[Range[1000], Mod[FromDigits[Reverse[IntegerDigits[ (#)^2 ]]],# ]==0 & ] Select[Range[8000],Divisible[IntegerReverse[#^2],#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 12 2016 *)
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PARI
isok(k) = !(fromdigits(Vecrev(digits(k^2))) % k); \\ Michel Marcus, Aug 20 2021
Extensions
Edited by Charles R Greathouse IV, Aug 02 2010