A099165 Palindromic in bases 10 and 32.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 66, 99, 363, 858, 1441, 2882, 5445, 6886, 9449, 15951, 19891, 21012, 29692, 32223, 54945, 369963, 477774, 564465, 585585, 609906, 672276, 717717, 780087, 804408, 912219, 1251521, 2639362, 3825283

Offset

1,3

Links

Ray Chandler and Robert G. Wilson v, Table of n, a(n) for n = 1..115, terms a(88)-a(111) from Ray Chandler.

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, 32], AppendTo[l, a]], {n, 10000}]; l
Select[Range[0, 10^5],
PalindromeQ[#] && # == IntegerReverse[#, 32] &] (* 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): # unordered generator of palindromes of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, 10**l):
            s = str(x)
            yield int(s+s[-2::-1])
            yield int(s+s[::-1])
A099165_list = sorted([n for n in palQgen10(6) if palQ(n, 32)])
# Chai Wah Wu, Nov 25 2014

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855.

Sequence in context: A370052 A082208 A201061 * A239480 A117055 A117056

Adjacent sequences: A099162 A099163 A099164 * A099166 A099167 A099168

Keyword

base,nonn

Author

Robert G. Wilson v, Sep 30 2004

Status

approved