A184988 Largest palindromic substring of n^2.

0, 1, 4, 9, 6, 5, 6, 9, 6, 8, 1, 121, 44, 9, 9, 22, 6, 9, 4, 6, 4, 44, 484, 9, 7, 6, 676, 9, 8, 8, 9, 9, 4, 9, 11, 22, 9, 9, 444, 5, 6, 8, 7, 9, 9, 202, 11, 22, 4, 4, 5, 6, 7, 9, 9, 5, 313, 9, 33, 8, 6, 7, 44, 969, 9, 22, 6, 44, 6, 7, 9, 5, 8, 9, 7, 6, 77, 929

Offset: 0

Author

Jonathan Vos Post, Mar 27 2011

Keywords

• nonn
• base
• easy
• look

Comments

Leading 0's are not allowed, so a(103) = 9, not 060. - Robert Israel, Nov 05 2020

Examples

			a(15) = largest palindromic substring of 15^2 = largest palindromic substring of 225 = 22.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A002113, A047813.

Programs

Maple

g:= proc(S) S[1] <> "0" and S = StringTools:-Reverse(S) end proc:
f:= proc(n) local S,d,l,i,Q;
  S:= sprintf("%d",n^2);
  d:= length(S);
  for l from d to 1 by -1 do
    Q:= select(g, [seq(S[i..i+l-1],i=1..d+1-l)]);
    if Q <> [] then return op(sscanf(max(Q),"%d")) fi
  od;
end proc:
f(0):= 0:
map(f, [$0..200]); # Robert Israel, Nov 05 2020

Formula

a(n) = A047813(A000290(n)).