A043036 - OEIS

A043036

Base 10 palindromes that start with 1.

1, 11, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 10001, 10101, 10201, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 11011, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Union of A222723 (palindromic primes starting with a digit 1) and A222724 (palindromic nonprime numbers starting with a digit 1). - Jaroslav Krizek, Mar 03 2013

LINKS

Harvey P. Dale and Jaroslav Krizek, Table of n, a(n) for n = 1..2222 (first 1000 terms from Harvey P. Dale)

MATHEMATICA

palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[0, 20000], IntegerDigits[#][[1]] == 1 && palQ[#, 10] &] (* T. D. Noe, Mar 12 2013 *)

Select[Range[20000], PalindromeQ[#]&&Mod[#, 10]==1&] (* Harvey P. Dale, May 12 2026 *)

PROG

(Python)

from itertools import count, islice, product

def agen(): # generator of terms

yield 1

for d in count(2):

for r in product("0123456789", repeat=d//2-1):

left = "1" + "".join(r)

for mid in ([[""], "0123456789"][d&1]):

yield int(left + mid + left[::-1])

print(list(islice(agen(), 42))) # Michael S. Branicky, Nov 04 2025

CROSSREFS

Cf. A002113 (palindromes in base 10).

Sequence in context: A115824 A364326 A208259 * A072001 A265510 A265528

Adjacent sequences: A043033 A043034 A043035 * A043037 A043038 A043039

KEYWORD

nonn,base,changed

AUTHOR

Clark Kimberling

STATUS

approved