A249156 - OEIS

%I #33 Apr 09 2020 10:28:00

%S 0,1,2,3,4,6,24,57,78,114,342,624,856,1432,10308,12654,27616,100056,

%T 537856,593836,769621,1434168,1473368,1636104,1823544,1862744,

%U 17968646,18108296,22412057,34713713,34853363,39280254,159690408,663706192

%N Palindromic in bases 5 and 7.

%C Intersection of A029952 and A029954.

%H G. Resta, <a href="/A249156/b249156.txt">Table of n, a(n) for n = 1..72</a> (first 60 terms from Ray Chandler)

%H Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On Simultaneous Palindromes</a>, arXiv:1403.0787 [math.NT], 2014.

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

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

%o (Python)

%o from gmpy2 import digits

%o def palQ(n,b): # check if n is a palindrome in base b

%o     s = digits(n,b)

%o     return s == s[::-1]

%o def palQgen(l,b): # unordered generator of palindromes in base b of length <= 2*l

%o     if l > 0:

%o         yield 0

%o         for x in range(1,b**l):

%o             s = digits(x,b)

%o             yield int(s+s[-2::-1],b)

%o             yield int(s+s[::-1],b)

%o A249156_list = sorted([n for n in palQgen(8,5) if palQ(n,7)]) # _Chai Wah Wu_, Nov 25 2014

%o (PARI) isok(n) = my(df = digits(n, 5), ds = digits(n, 7)); (Vecrev(df)==df) && (Vecrev(ds)==ds); \\ _Michel Marcus_, Oct 31 2017

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

%K nonn,base

%O 1,3

%A _Ray Chandler_, Oct 27 2014