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

1,3

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]

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)
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

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

Sequence in context: A133476 A131023 A069514 * A101012 A048659 A065774

Adjacent sequences: A249152 A249153 A249154 * A249156 A249157 A249158

Keyword

nonn,base

Author

Ray Chandler, Oct 27 2014

Status

approved