A196510 - OEIS

%I #30 Jan 16 2022 15:46:22

%S 6643,4,10,26,28,8,121,10,121,244,13,28,1210,16,68,784,1733,20,1604,

%T 242,23,2096,100,26,937,28,203,3280,1952,160,1249,68,280,1366,14483,

%U 608,11293,40,82,5948,7102,484,2069,644,1222,4372,784,100,6452,52

%N Smallest number greater than n that is palindromic in base 3 and base n.

%H Zak Seidov, <a href="/A196510/b196510.txt">Table of n, a(n) for n = 2..1000</a>

%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0699.html">Problem of the month June 1999</a>

%p ispal := proc(n,b)

%p         dgs := convert(n,base,b) ;

%p         for i from 1 to nops(dgs)/2 do

%p                 if op(i,dgs) <> op(-i,dgs) then

%p                         return false;

%p                 end if;

%p         end do;

%p         return true;

%p end proc:

%p A196510 := proc(n)

%p         for k from n+1 do

%p                 if ispal(k,n) and ispal(k,3) then

%p                         return k;

%p                 end if;

%p         end do:

%p end proc:

%p seq(A196510(n),n=2..30) ; # _R. J. Mathar_, Oct 13 2011

%t pal3n[n_]:=Module[{k=n+1},While[IntegerDigits[k,3]!=Reverse[ IntegerDigits[ k,3]] || IntegerDigits[ k,n]!= Reverse[ IntegerDigits[k,n]],k++];k]; Array[ pal3n,60,2] (* _Harvey P. Dale_, Jan 16 2022 *)

%o (Sage)

%o def A196510(n):

%o     is_palindrome = lambda x,b=10: x.digits(b) == (x.digits(b))[::-1]

%o     return next(k for k in IntegerRange(n+1, infinity) if is_palindrome(k,n) and is_palindrome(k,3))

%o # _D. S. McNeil_, Oct 03 2011

%Y Cf. A056749.

%K nonn,base

%O 2,1

%A _Kausthub Gudipati_, Oct 03 2011