A249158 Palindromic in bases 7 and 29.

0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 150, 300, 5952, 7752, 7955, 9755, 9958, 11904, 13704, 13907, 14110, 15707, 15910, 392850, 751043, 4585544, 12737804, 12828748, 16380296, 19289406, 19380350, 20228253, 33115710, 395849700, 1339182534

Offset: 1

Author

Ray Chandler, Oct 27 2014

Keywords

• nonn
• base

Examples

			150 is a term since 150 = 303 base 7 and 150 = 55 base 27.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..80 (terms < 10^18)
• Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Crossrefs

Cf. A007632, A060792, A249155, A249156, A249157.

Programs

Mathematica

palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,7]&&palQ[#,29]&]

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): # unordered generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, b**l):
            s = digits(x, b)
            yield int(s+s[-2::-1], b)
            yield int(s+s[::-1], b)
A249158_list = sorted([n for n in palQgen(8,7) if palQ(n,29)])
# Chai Wah Wu, Nov 25 2014