A088882 Nontrivial palindromes in base 10 (i.e., palindromes that are not RepDigits such as 3, 111, 22222, or 888888888).

101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 565, 575, 585, 595, 606, 616, 626, 636, 646, 656, 676

Offset: 1

Author

Chuck Seggelin, Oct 21 2003

Keywords

• base
• nonn

Comments

The early portion of this sequence appears to be very similar to the early portions of two other sequences. Note that a(n) = A046075(n) for n = 1..81. A046075 deals with nontrivial undulants of 3 digits or more which by definition excludes RepDigits, but which includes non-palindromic terms when 4-digit numbers are reached. For example a(82) = 1001 but A046075(82) = 1010. Note also that a(n) = A050783(n+10) for n = 1..81. A050783 deals with palindromes that contain no consecutive pairs of equal digits, so although A050783 excludes RepDigits, it includes the single-digit palindromes and excludes a large number of the palindromes in this sequence (such as, for example, all the 4-digit nontrivial palindromes and larger nontrivial palindromes such as 22022 or 61116). A050783(92) = 10101. Note that in the first 65534 values of n there are 754 palindromes, 712 nontrivial palindromes and 42 RepDigits.

Examples

			a(4) = 141 because 141 is the fourth term of the sequence of base-10 palindromes (A002113) that does not appear in the sequence of RepDigits (A010785).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113 (base-10 palindromes), A010785 (repdigits), A046075 (nontrivial undulants), A050783 (palindromes with no pair of consecutive equal digits).

Programs

Python

from itertools import count, islice, product
def agen(): # generator of terms
    digits = "0123456789"
    for d in count(3):
        for p in product(digits, repeat=d//2):
            if d > 1 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], digits][d%2]:
                t = left + mid + right
                if len(set(t)) != 1: yield int(t)
print(list(islice(agen(), 52))) # Michael S. Branicky, May 17 2022