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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 (list; graph; refs; listen; history; text; internal format)
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]

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

Cf. A007632, A060792, A249155, A249156, A249158.

Sequence in context: A068862 A061729 A286126 * A033621 A332808 A108548

Adjacent sequences:  A249154 A249155 A249156 * A249158 A249159 A249160

KEYWORD

nonn,base

AUTHOR

Ray Chandler, Oct 27 2014

STATUS

approved

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)