A050430 Length of longest palindromic subword of (n base 2).

1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 3, 5, 4, 3, 3, 4, 3, 5, 3, 3, 4, 5, 5, 6, 5, 5, 5, 4, 4, 4, 3, 4, 5, 5, 4, 6, 5, 4, 4, 5, 4, 6, 3, 5, 5, 5, 3, 4, 3, 5, 4, 4, 5, 6, 6, 7, 6, 6, 5, 5, 5, 5, 5, 7, 5, 4, 6, 4, 5, 4, 4, 5, 6, 4, 5, 7, 5, 5, 4, 4, 6, 6, 5, 7, 6, 5, 5, 6, 5, 7, 5, 4, 6, 6, 3, 4

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

a(A083318(n-1)) = n; a(A193159(k)) = 3, 1 <= k <= 26. [Reinhard Zumkeller, Jul 17 2011]

Examples

			(11 base 2) = 1011, containing the palindrome 101, therefore a(11) = 3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..16385 = 2^14 + 1

Crossrefs

Cf. A007088; A050431 (base 3), A050432 (base 4), A050433 (base 5).

Cf. A215244, A215467, A215256.

Programs

Haskell

import Data.Char (intToDigit, digitToInt)
import Numeric (showIntAtBase)
a050430 n = a050430_list !! (n-1)
a050430_list = f 1 where
   f n = g (showIntAtBase 2 intToDigit n "") : f (n+1)
   g zs | zs == reverse zs = length zs
        | otherwise        = max (h $ init zs) (h $ tail zs)
   h zs@('0':_) = g zs
   h zs@('1':_) = a050430 $ foldl (\v d -> digitToInt d + 2*v) 0 zs
-- Reinhard Zumkeller, Jul 16 2011

Maple

# A050430 Length of longest palindromic factor of n for n in [M1..M2] - from N. J. A. Sloane, Aug 07 2012, revised Aug 11 2012
isPal := proc(L)
    local d ;
    for d from 1 to nops(L)/2 do
        if op(d, L) <> op(-d, L) then
            return false;
        end if;
    end do:
    return true;
end proc:
# start of main program
ans:=[];
M1:=0; M2:=64;
for n from M1 to M2 do
t1:=convert(n,base,2);
rec:=0:
l1:=nops(t1);
for j1 from 0 to l1-1 do
for j2 from j1+1 to l1 do
F1 := [op(j1+1..j2,t1)];
if (isPal(F1) and j2-j1>rec) then rec:=j2-j1; fi;
od:
od:
ans:=[op(ans),rec]:
od:
ans;

Mathematica

f[n_] := Block[{id = IntegerDigits[n, 2]}, k = Length@ id; While[ Union[# == Reverse@# & /@ Partition[id, k, 1]][[-1]] != True, k--]; k]; Array[f, 105] (* Robert G. Wilson v, Jul 16 2011 *)

Formula

a(n) <= min(a(2*n), a(2*n+1)). [Reinhard Zumkeller, Jul 31 2011]

Extensions

Extended by Ray Chandler, Mar 11 2010