A342942 Numbers whose palindromization is a perfect power.

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

Michel Marcus, Table of n, a(n) for n = 1..100

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

Cf. A075786, A076443, A001597, A002113, A342803.

Sequence in context: A307279 A106323 A177796 * A322462 A037304 A041298

Adjacent sequences: A342939 A342940 A342941 * A342943 A342944 A342945

Keyword

nonn,base

Author

Michel Marcus, Mar 30 2021

Status

approved