A249156 Palindromic in bases 5 and 7.

0, 1, 2, 3, 4, 6, 24, 57, 78, 114, 342, 624, 856, 1432, 10308, 12654, 27616, 100056, 537856, 593836, 769621, 1434168, 1473368, 1636104, 1823544, 1862744, 17968646, 18108296, 22412057, 34713713, 34853363, 39280254, 159690408, 663706192

Offset: 1

Author

Ray Chandler, Oct 27 2014

Keywords

• nonn
• base

Comments

Intersection of A029952 and A029954.

Examples

			114 is a term since 114 = 424 base 5 and 114 = 222 base 7.
		

Links

• G. Resta, Table of n, a(n) for n = 1..72 (first 60 terms from Ray Chandler)
• Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Crossrefs

Cf. A007632, A060792, A249155, A249157, A249158.

Programs

Mathematica

palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,5]&&palQ[#,7]&]

PARI

isok(n) = my(df = digits(n, 5), ds = digits(n, 7)); (Vecrev(df)==df) && (Vecrev(ds)==ds); \\ Michel Marcus, Oct 31 2017

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)
A249156_list = sorted([n for n in palQgen(8,5) if palQ(n,7)]) # Chai Wah Wu, Nov 25 2014