A029968 Palindromic in bases 13 and 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 222, 313, 353, 444, 575, 666, 797, 1111, 6776, 8778, 24542, 25452, 26362, 56265, 311113, 2377732, 2713172, 2832382, 2906092, 8864688, 10122101, 13055031, 20244202, 20944902, 23177132, 23877832

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..76

P. De Geest, Palindromic numbers beyond base 10

Mathematica

NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]] ]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]] ]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[idfhn]], Mod[l, 2]] ]]] ]]]; palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 13], AppendTo[l, a]], {n, 100000}]; l (* Robert G. Wilson v, Sep 03 2004 *)
Select[Range[0, 10^5],
PalindromeQ[#] && # == IntegerReverse[#, 13] &] (* Robert Price, Nov 09 2019 *)

Prog

(Python)
from gmpy2 import digits
def palQ(n, b): # check if n is a palindrome in base b
    s = digits(n, b)
    return s == s[::-1]
def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, l+1):
            for y in range(10**(x-1), 10**x):
                s = str(y)
                yield int(s+s[-2::-1])
            for y in range(10**(x-1), 10**x):
                s = str(y)
                yield int(s+s[::-1])
A029968_list = [n for n in palQgen10(9) if palQ(n, 13)]
# Chai Wah Wu, Dec 01 2014

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029969, A029970, A029731, A097855, A099165.

Sequence in context: A239090 A248889 A029967 * A097855 A250408 A029969

Adjacent sequences: A029965 A029966 A029967 * A029969 A029970 A029971

Keyword

nonn,base

Author

Patrick De Geest

Status

approved