A056142 Concatenate n, floor[n/10], floor[n/100] ... (but do not continue if floor[.]=0).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555

Offset: 0

Author

Henry Bottomley, Jun 15 2000

Keywords

• base
• easy
• nonn

Comments

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

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

Crossrefs

Cf. A002113, A056143, A056525.

Programs

Mathematica

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