

A068061


Palindromic numbers j that are not of the form k + reverse(k) for any k.


2



1, 3, 5, 7, 9, 111, 131, 151, 171, 191, 212, 232, 252, 272, 292, 313, 333, 353, 373, 393, 414, 434, 454, 474, 494, 515, 535, 555, 575, 595, 616, 636, 656, 676, 696, 717, 737, 757, 777, 797, 818, 838, 858, 878, 898, 919, 939, 959, 979, 999, 10101, 10301, 10501
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Intersection of A002113 and A067031. Every palindrome with an even number of digits is of the form k + reverse(k), for example 123321 = 123000 + 000321, so the sequence has no terms with an even number of digits.
It seems that the terms follow a strict pattern: x1x', x3x', x5x', x7x', x9x', y1y', y3y', y5y', y7y', y9y' and so on. x' is reverse(x). Apart from the first 5 terms in the sequence, the surrounding terms (x and y) simply iterate over the positive integers.  Dmitry Kamenetsky, Mar 10 2017
Every palindrome with an odd number of digits is of the form k + reverse(k) if the central digit is even, for example 1234321 = 1232000 + 0002321, so no term with an odd number of digits has an even central digit.  A.H.M. Smeets, Feb 01 2019


LINKS



EXAMPLE

9 belongs to this sequence, since there is no k such that k + reverse(k) = 9 (cf. A067031).


PROG

(PARI) isok(n) = {if (Pol(d=digits(n)) == Polrev(d), for (k=1, n1, if (k + fromdigits(Vecrev(digits(k))) == n, return (0)); ); 1; ); } \\ Michel Marcus, Mar 12 2017


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



STATUS

approved



