A196510 Smallest number greater than n that is palindromic in base 3 and base n.

6643, 4, 10, 26, 28, 8, 121, 10, 121, 244, 13, 28, 1210, 16, 68, 784, 1733, 20, 1604, 242, 23, 2096, 100, 26, 937, 28, 203, 3280, 1952, 160, 1249, 68, 280, 1366, 14483, 608, 11293, 40, 82, 5948, 7102, 484, 2069, 644, 1222, 4372, 784, 100, 6452, 52

Offset: 2

Author

Kausthub Gudipati, Oct 03 2011

Keywords

• nonn
• base

Links

• Zak Seidov, Table of n, a(n) for n = 2..1000
• Erich Friedman, Problem of the month June 1999

Crossrefs

Cf. A056749.

Programs

Maple

ispal := proc(n,b)
        dgs := convert(n,base,b) ;
        for i from 1 to nops(dgs)/2 do
                if op(i,dgs) <> op(-i,dgs) then
                        return false;
                end if;
        end do;
        return true;
end proc:
A196510 := proc(n)
        for k from n+1 do
                if ispal(k,n) and ispal(k,3) then
                        return k;
                end if;
        end do:
end proc:
seq(A196510(n),n=2..30) ; # R. J. Mathar, Oct 13 2011

Mathematica

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 *)

Sage

def A196510(n):
    is_palindrome = lambda x,b=10: x.digits(b) == (x.digits(b))[::-1]
    return next(k for k in IntegerRange(n+1, infinity) if is_palindrome(k,n) and is_palindrome(k,3))
# D. S. McNeil, Oct 03 2011