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A050430 Length of longest palindromic subword of (n base 2). 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

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

Cf. A215244, A215467, A215256.

Sequence in context: A063787 A182745 A129843 * A277329 A071330 A092333

Adjacent sequences:  A050427 A050428 A050429 * A050431 A050432 A050433

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Ray Chandler, Mar 11 2010

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)