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A342942
Numbers whose palindromization is a perfect power.
2
12, 13, 34, 48, 67, 102, 123, 146, 408, 449, 696, 698, 942, 1002, 1030, 1234, 1367, 4008, 5221, 6948, 10002, 10030, 10203, 10406, 12124, 12345, 12568, 40008, 40409, 52280, 61732, 94206, 100002, 102214, 106625, 121024, 123456, 400008, 637832, 1000002, 1000300, 1002003
OFFSET
1,1
COMMENTS
Palindromization is the function that extends the string representation of a number into a palindrome.
Even palindromization is the concatenation of a number and its reversal. Odd palindromization excludes the first digit of the reversal.
LINKS
EXAMPLE
12 is a term because 121 is a square.
13 is a term because 1331 is a cube.
MATHEMATICA
Select[Range[10, 50000], Or@@(GCD@@Last/@FactorInteger@#>1&/@FromDigits/@(Join[a, Reverse@#]&/@{a=IntegerDigits@#, Most@a}))&] (* Giorgos Kalogeropoulos, Mar 30 2021 *)
PROG
(PARI) rev(x) = strjoin(Vecrev(Str(x)));
isok(m) = ispower(eval(Str(m, rev(m)))) || ispower(eval(Str(m, rev(m\10))));
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 30 2021
STATUS
approved