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A281625 Numbers m>0 such that m = k*(reversal of k*m) for some k<=m.

%I A281625 #26 Jul 26 2025 17:54:19
%S A281625 1,2,3,4,5,6,7,8,9,10,11,20,22,30,33,40,44,50,55,60,66,70,77,80,88,90,
%T A281625 99,100,101,110,111,121,131,141,151,161,171,181,191,200,202,212,220,
%U A281625 222,232,242,252,262,272,282,292,300,303,313,323,330,333,343,353
%N A281625 Numbers m>0 such that m = k*(reversal of k*m) for some k<=m.
%C A281625 Generalization of palindrome numbers in base 10.
%C A281625 Sequence is not the same as A061917 or A169824; a(188) = 3267 is not a term of these sequences.
%C A281625 Supersequence of A002113 (palindromes in base 10) and A061917.
%C A281625 Sequences a(n)_k of numbers m such that m = k*(reversal of k*m) for k <= 30 and n >= 1:
%C A281625 a(n)_1 = A002113(n+1) (palindromes > 0 in base 10);
%C A281625 a(n)_2 = 4356, 43956, 439956, 4399956, 43999956, 439999956, ...;
%C A281625 a(n)_3 = 3267, 32967, 329967, 3299967, 32999967, 329999967, ...;
%C A281625 a(n)_5 = a(n)_20 = 10*a(n)_2 = 43560, 439560, 4399560, 43999560, ...;
%C A281625 a(n)_8 = 6600, 6606600, 66006600, 660006600, ...;
%C A281625 a(n)_10 = 10*A002113(n+1): 10, 20, 30, 40, 50, 60, 70, 80, 90, 110, ... ;
%C A281625 a(n)_30 = 10*a(n)_3 = 32670, 329670, 3299670, 32999670, ...
%H A281625 Jaroslav Krizek, <a href="/A281625/b281625.txt">Table of n <= 5000</a>
%e A281625 3267 is in the sequence because 3267 = 3*(reversal of 3*3267) = 3*(reversal of 9801) = 3*1089.
%p A281625 read("transforms") :
%p A281625 isA281625 := proc(n)
%p A281625     for k from 1 to n do
%p A281625         if k*digrev(k*n) = n then
%p A281625             return true ;
%p A281625         end if;
%p A281625     end do:
%p A281625     false;
%p A281625 end proc:
%p A281625 A281625 := proc(n)
%p A281625     option remember ;
%p A281625     if n = 1 then
%p A281625         1;
%p A281625     else
%p A281625         for a from procname(n-1)+1 do
%p A281625             if isA281625(a) then
%p A281625                 return a;
%p A281625             end if;
%p A281625         end do:
%p A281625     end if;
%p A281625 end proc:
%p A281625 seq(A281625(n),n=1..100) ; # _R. J. Mathar_, Aug 06 2019
%t A281625 Select[Range@ 353, Function[n, Total@ Boole@ Map[Function[k, n == k FromDigits@ Reverse[IntegerDigits[k n]]], Range@ n] > 0]] (* _Michael De Vlieger_, Feb 11 2017 *)
%o A281625 (Magma) [n: k in [1..n], n in [1..1000] | n eq k * Seqint(Reverse(Intseq(k*n)))];
%Y A281625 Cf. A061917, A002113, A169824.
%K A281625 nonn,base
%O A281625 1,2
%A A281625 _Jaroslav Krizek_, Feb 11 2017