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A249155
Palindromic in bases 6 and 15.
4
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
1,3
COMMENTS
Intersection of A029953 and A029960.
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.
EXAMPLE
301 is a term since 301 = 1221 base 6 and 301 = 151 base 15.
MATHEMATICA
palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[10^6] - 1, palQ[#, 6] && palQ[#, 15] &]
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): # 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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ray Chandler, Oct 27 2014
STATUS
approved