A056142 - OEIS

%I #9 Jul 11 2020 20:03:07

%S 0,1,2,3,4,5,6,7,8,9,101,111,121,131,141,151,161,171,181,191,202,212,

%T 222,232,242,252,262,272,282,292,303,313,323,333,343,353,363,373,383,

%U 393,404,414,424,434,444,454,464,474,484,494,505,515,525,535,545,555

%N Concatenate n, floor[n/10], floor[n/100] ... (but do not continue if floor[.]=0).

%C For 0 < n < 100, a(n) = A056525(n). If n has 3 digits, then a(n) is a palindrome if and only if n is. If n has 4 or 5 digits, then a(n) is a palindrome if and only if all digits of n are equal. - _David Wasserman_, May 23 2005

%C Conjecture: if n has 3 or more digits, a(n) is a palindrome only if all the digits of n are the same. It is easy to see that any palindrome can have at most 2 distinct digits: matching digits from the initial n in the concatenation matches each digit after the second with an earlier digit. - _Franklin T. Adams-Watters_, Sep 07 2006

%t Table[FromDigits[Flatten[IntegerDigits/@DeleteCases[Floor[n/10^Range[ 0,5]],0]]],{n,0,60}] (* _Harvey P. Dale_, Jul 11 2020 *)

%Y Cf. A002113, A056143, A056525.

%K base,easy,nonn

%O 0,3

%A _Henry Bottomley_, Jun 15 2000