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A249157
Palindromic in bases 11 and 13.
4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 84, 366, 510, 732, 876, 1020, 1098, 1242, 1464, 10248, 30252, 31110, 62220, 103704, 146541, 3382050, 3698730, 4391268, 225622530, 272466250, 413186676, 713998530, 801837204, 848770222, 912265732
OFFSET
1,3
COMMENTS
Intersection of A029956 and A029958.
LINKS
Ray Chandler, Table of n, a(n) for n = 1..69 (terms < 10^18)
Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.
EXAMPLE
366 is a term since 366 = 303 base 11 and 366 = 222 base 13.
MATHEMATICA
palQ[n_Integer, base_Integer]:=Block[{idn=IntegerDigits[n, base]}, idn==Reverse[idn]]; Select[Range[10^6]-1, palQ[#, 11]&&palQ[#, 13]&]
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 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)
A249157_list = sorted([n for n in palQgen(6, 11) if palQ(n, 13)]) # Chai Wah Wu, Nov 25 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ray Chandler, Oct 27 2014
STATUS
approved