A029804 Numbers that are palindromic in bases 8 and 10.

0, 1, 2, 3, 4, 5, 6, 7, 9, 121, 292, 333, 373, 414, 585, 3663, 8778, 13131, 13331, 26462, 26662, 30103, 30303, 207702, 628826, 660066, 1496941, 1935391, 1970791, 4198914, 55366355, 130535031, 532898235, 719848917, 799535997, 1820330281

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Intersection of A002113 and A029803. - Michel Marcus, Nov 20 2014

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..75
• Patrick De Geest, Palindromic numbers beyond base 10
• Rick Regan, Code to generate this sequence

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165.

Programs

Magma

[n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 8) eq Reverse(Intseq(n, 8))]; // Vincenzo Librandi, Nov 23 2014

Mathematica

b1=8; b2=10; lst={}; Do[d1=IntegerDigits[n, b1];d2=IntegerDigits[n,b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 100000}]; lst (* Vincenzo Librandi, Nov 13 2014 *)
Select[Range[0,1820331000],PalindromeQ[#]&&IntegerDigits[#,8] == Reverse[ IntegerDigits[#,8]]&] (* Harvey P. Dale, Mar 18 2019 *)

PARI

isok(n) = (n==0) || ((d10=digits(n, 10)) && (d10==Vecrev(d10)) && (d8=digits(n, 8)) && (d8==Vecrev(d8))); \\ Michel Marcus, Nov 13 2014

PARI

ispal(n,r) = my(d=digits(n,r)); d==Vecrev(d);
for(n=0,10^7,if(ispal(n,10)&&ispal(n,8),print1(n,", "))); \\ Joerg Arndt, Nov 22 2014

Python

def palQ8(n): # check if n is a palindrome in base 8
    s = oct(n)[2:]
    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])
A029804_list = sorted([n for n in palQgen10(6) if palQ8(n)])
# Chai Wah Wu, Nov 25 2014

Extensions

More terms from Robert G. Wilson v, Sep 30 2004

Incorrect Mathematica program deleted by N. J. A. Sloane, Sep 01 2009

Terms 33 through 36 corrected by Rick Regan (exploringbinary(AT)gmail.com), Sep 01 2009