A333770 Smallest palindromic number >= 3^n.

1, 3, 9, 33, 88, 252, 737, 2222, 6666, 19691, 59095, 177771, 532235, 1594951, 4783874, 14355341, 43055034, 129141921, 387424783, 1162332611, 3486886843, 10460406401, 31381118313, 94143234149, 282429924282, 847288882748

Offset: 0

Author

Eder Vanzei, Apr 04 2020

Keywords

• easy
• nonn
• base

Examples

			a(10) = 59095, because 3^10 = 59049 and 59095 is the smallest palindromic number >= 59049.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..2093

Crossrefs

Cf. A000244, A002113, A262038, A333016.

Programs

Maple

digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
f:= proc(n) local d,x,y,t;
  d:= ilog10(n)+1;
  if d::even then
    x:= floor(n/10^(d/2));
    t:= x*10^(d/2)+digrev(x);
    if t >= n then return t fi;
    (x+1)*10^(d/2)+digrev(x+1);
  else
    x:= floor(n/10^((d-1)/2));
    t:= x*10^((d-1)/2)+digrev(floor(x/10));
    if t >= n then return t fi;
    y:= x mod 10;
    if y < 9 then return t + 10^((d-1)/2) fi;
    x:= x+1;
    x*10^((d-1)/2)+digrev(floor(x/10));
  fi
end proc:
seq(f(3^i),i=0..30); # Robert Israel, May 04 2020

PARI

a(n) = for(k=3^n, oo, if(Vecrev(v=digits(k))==v, return(k)));

Formula

a(n) = A262038(A000244(n)). - Michel Marcus, May 04 2020