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A281625
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Numbers n>0 such that n = k*(reversal of k*n) for some k<=n.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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, ...
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LINKS
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EXAMPLE
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3267 is in the sequence because 3267 = 3*(reversal of 3*3267) = 3*(reversal of 9801) = 3*1089.
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MAPLE
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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:
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:
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MATHEMATICA
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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 *)
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PROG
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(Magma) [n: k in [1..n], n in [1..1000] | n eq k * Seqint(Reverse(Intseq(k*n)))]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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