A249155 Palindromic in bases 6 and 15.

0, 1, 2, 3, 4, 5, 7, 14, 80, 160, 301, 602, 693, 994, 1295, 1627, 1777, 2365, 2666, 5296, 5776, 6256, 17360, 34720, 51301, 52201, 105092, 155493, 209284, 587846, 735644, 7904800, 11495701, 80005507, 80469907, 83165017, 89731777, 90196177

Offset: 1

Author

Ray Chandler, Oct 27 2014

Keywords

• nonn
• base

Comments

Intersection of A029953 and A029960.

Examples

			301 is a term since 301 = 1221 base 6 and 301 = 151 base 15.
		

Links

• Ray Chandler and Chai Wah Wu, Table of n, a(n) for n = 1..71 (terms < 6^28). First 65 terms from Ray Chandler.
• Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Crossrefs

Cf. A007632, A060792, A249156, A249157, A249158.

Programs

Mathematica

palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[10^6] - 1, palQ[#, 6] && palQ[#, 15] &]

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 palQgen(l, b): # generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, l+1):
            for y in range(b**(x-1), b**x):
                s = digits(y, b)
                yield int(s+s[-2::-1], b)
            for y in range(b**(x-1), b**x):
                s = digits(y, b)
                yield int(s+s[::-1], b)
A249155_list = [n for n in palQgen(8, 6) if palQ(n, 15)] # Chai Wah Wu, Nov 29 2014