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A029731 Palindromic in bases 10 and 16.

%I A029731 #36 Mar 23 2020 03:02:02
%S A029731 0,1,2,3,4,5,6,7,8,9,11,353,626,787,979,1991,3003,39593,41514,90209,
%T A029731 94049,96369,98689,333333,512215,666666,749947,845548,1612161,2485842,
%U A029731 5614165,6487846,9616169,67433476,90999909,94355349,94544549,119919911
%N A029731 Palindromic in bases 10 and 16.
%H A029731 Robert G. Wilson v, <a href="/A029731/b029731.txt">Table of n, a(n) for n = 1..81</a>
%H A029731 Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>
%p A029731 N:= 9: # to get all terms with up to N decimal digits
%p A029731 qpali:= proc(k, b) local L; L:= convert(k, base, b); if L = ListTools:-Reverse(L) then k else NULL fi end proc:
%p A029731 digrev:= proc(k,b) local L,n; L:= convert(k,base,b); n:= nops(L); add(L[i]*b^(n-i),i=1..n); end proc:
%p A029731 Res:= $0..9:
%p A029731 for d from 2 to N do
%p A029731   if d::even then
%p A029731     m:= d/2;
%p A029731     Res:= Res, seq(qpali(n*10^m + digrev(n,10),16), n=10^(m-1)..10^m-1);
%p A029731   else
%p A029731     m:= (d-1)/2;
%p A029731     Res:= Res, seq(seq(qpali(n*10^(m+1)+y*10^m+digrev(n,10),16), y=0..9), n=10^(m-1)..10^m-1);
%p A029731   fi
%p A029731 od:
%p A029731 Res; # _Robert Israel_, Nov 23 2014
%t A029731 A029731Q = PalindromeQ@# && IntegerReverse[#, 16] == # &; Select[Range[10^5], A029731Q] (* _JungHwan Min_, Mar 02 2017 *)
%t A029731 Select[Range[10^7], Times @@ Boole@ Map[# == Reverse@ # &, {IntegerDigits@ #, IntegerDigits[#, 16]}] > 0 &] (* _Michael De Vlieger_, Mar 03 2017 *)
%o A029731 (Python)
%o A029731 def palQ16(n): # check if n is a palindrome in base 16
%o A029731     s = hex(n)[2:]
%o A029731     return s == s[::-1]
%o A029731 def palQgen10(l): # unordered generator of palindromes of length <= 2*l
%o A029731     if l > 0:
%o A029731         yield 0
%o A029731         for x in range(1,10**l):
%o A029731             s = str(x)
%o A029731             yield int(s+s[-2::-1])
%o A029731             yield int(s+s[::-1])
%o A029731 A029731_list = sorted([n for n in palQgen10(6) if palQ16(n)])
%o A029731 # _Chai Wah Wu_, Nov 25 2014
%Y A029731 Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A097855, A099165.
%K A029731 nonn,base
%O A029731 1,3
%A A029731 _Patrick De Geest_