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A088882
Nontrivial palindromes in base 10 (i.e., palindromes that are not RepDigits such as 3, 111, 22222, or 888888888).
3
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
1,1
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.
LINKS
EXAMPLE
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).
PROG
(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
CROSSREFS
Cf. A002113 (base-10 palindromes), A010785 (repdigits), A046075 (nontrivial undulants), A050783 (palindromes with no pair of consecutive equal digits).
Sequence in context: A182693 A328996 A046075 * A261453 A135602 A095635
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 21 2003
STATUS
approved