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

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, 99, 100, 101, 110, 111, 121, 131, 141, 151, 161, 171, 181, 191, 200, 202, 212, 220, 222, 232, 242, 252, 262, 272, 282, 292, 300, 303, 313, 323, 330, 333, 343, 353

Offset: 1

Author

Jaroslav Krizek, Feb 11 2017

Keywords

• nonn
• base

Comments

Generalization of palindrome numbers in base 10.

Sequence is not the same as A061917 or A169824; a(188) = 3267 is not a term of these sequences.

Supersequence of A002113 (palindromes in base 10) and A061917.

Sequences a(n)_k of numbers m such that m = k*(reversal of k*m) for k <= 30 and n >= 1:

a(n)_1 = A002113(n+1) (palindromes > 0 in base 10);

a(n)_2 = 4356, 43956, 439956, 4399956, 43999956, 439999956, ...;

a(n)_3 = 3267, 32967, 329967, 3299967, 32999967, 329999967, ...;

a(n)_5 = a(n)_20 = 10*a(n)_2 = 43560, 439560, 4399560, 43999560, ...;

a(n)_8 = 6600, 6606600, 66006600, 660006600, ...;

a(n)_10 = 10*A002113(n+1): 10, 20, 30, 40, 50, 60, 70, 80, 90, 110, ... ;

a(n)_30 = 10*a(n)_3 = 32670, 329670, 3299670, 32999670, ...

Examples

			3267 is in the sequence because 3267 = 3*(reversal of 3*3267) = 3*(reversal of 9801) = 3*1089.
		

Links

• Jaroslav Krizek, Table of n <= 5000

Crossrefs

Cf. A061917, A002113, A169824.

Programs

Magma

[n: k in [1..n], n in [1..1000] | n eq k * Seqint(Reverse(Intseq(k*n)))];

Maple

read("transforms") :
isA281625 := proc(n)
    for k from 1 to n do
        if k*digrev(k*n) = n then
            return true ;
        end if;
    end do:
    false;
end proc:
A281625 := proc(n)
    option remember ;
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if isA281625(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A281625(n),n=1..100) ; # R. J. Mathar, Aug 06 2019

Mathematica

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 *)