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Number of times n is palindromic in bases b, 2 <= b <= 10.
9

%I #18 Sep 09 2021 09:35:20

%S 9,9,8,8,7,7,5,5,4,3,3,1,1,1,1,2,2,2,2,0,2,3,1,1,2,1,2,2,2,1,1,2,1,2,

%T 1,1,2,1,1,0,3,1,1,1,1,2,2,0,1,1,2,2,2,0,1,3,1,2,0,1,1,1,1,3,1,3,1,2,

%U 1,0,1,1,1,2,1,0,0,1,2,0,3,1,2,1,0,3

%N Number of times n is palindromic in bases b, 2 <= b <= 10.

%H T. D. Noe, <a href="/A050812/b050812.txt">Table of n, a(n) for n = 0..10000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>

%e a(121) = 4 since 121_10, 171_8, 232_7 and 11111_3 are palindromes.

%t Table[Count[Table[IntegerDigits[n,b],{b,2,10}],_?(#==Reverse[#]&)],{n,0,90}] (* _Harvey P. Dale_, Aug 18 2012 *)

%o (Python)

%o from sympy.ntheory.digits import digits

%o def ispal(n, b):

%o digs = digits(n, b)[1:]

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

%o def a(n): return sum(ispal(n, b) for b in range(2, 11))

%o print([a(n) for n in range(87)]) # _Michael S. Branicky_, Sep 09 2021

%o (PARI) a(n) = sum(b=2, 10, my(d=digits(n, b)); d == Vecrev(d)); \\ _Michel Marcus_, Sep 09 2021

%Y Cf. A050813, A016038, A002113.

%K nonn,base

%O 0,1

%A _Patrick De Geest_, Oct 15 1999