login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265509 a(n) = largest base-2 palindrome m <= 2n+1 such that every base-2 digit of m is <= the corresponding digit of 2n+1; m is written in base 10. 70
1, 3, 5, 7, 9, 9, 9, 15, 17, 17, 21, 21, 17, 27, 21, 31, 33, 33, 33, 33, 33, 33, 45, 45, 33, 51, 33, 51, 33, 51, 45, 63, 65, 65, 65, 65, 73, 73, 73, 73, 65, 65, 85, 85, 73, 73, 93, 93, 65, 99, 65, 99, 73, 107, 73, 107, 65, 99, 85, 119, 73, 107, 93, 127, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 129, 153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A007088(a(n)) = A265510(n). - Reinhard Zumkeller, Dec 11 2015

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..8191

MAPLE

ispal := proc(n) # test for base-b palindrome

local L, Ln, i;

global b;

    L := convert(n, base, b);

    Ln := nops(L);

    for i to floor(1/2*Ln) do

        if L[i] <> L[Ln + 1 - i] then return false end if

    end do;

    return true

end proc

# find max pal <= n and in base-b shadow of n, write in base 10

under10:=proc(n) global b;

local t1, t2, i, m, sw1, L2;

if n mod b = 0 then return(0); fi;

t1:=convert(n, base, b);

for m from n by -1 to 0 do

if ispal(m) then

   t2:=convert(m, base, b);

   L2:=nops(t2);

   sw1:=1;

   for i from 1 to L2 do

      if t2[i] > t1[i] then sw1:=-1; break; fi;

                      od:

   if sw1=1 then return(m); fi;

fi;

                       od;

end proc;

b:=2; [seq(under10(2*n+1), n=0..144)]; # Gives A265509

# find max pal <= n and in base-b shadow of n, write in base b

underb:=proc(n) global b;

local t1, t2, i, m, mb, sw1, L2;

if n mod b = 0 then return(0); fi;

t1:=convert(n, base, b);

for m from n by -1 to 0 do

if ispal(m) then

   t2:=convert(m, base, b);

   L2:=nops(t2);

   sw1:=1;

   for i from 1 to L2 do

      if t2[i] > t1[i] then sw1:=-1; break; fi;

                      od:

   if sw1=1 then mb:=add(t2[i]*10^(i-1), i=1..L2); return(mb); fi;

fi;

                       od;

end proc;

b:=2; [seq(underb(2*n+1), n=0..144)]; # Gives A265510

MATHEMATICA

A265509 = FromDigits[Min /@ Transpose[{#, Reverse@#}], 2] &@IntegerDigits[2 # + 1, 2] & (* JungHwan Min, Aug 22 2016 *)

PROG

(Haskell)

a265509 n = a265509_list !! n

a265509_list = f (tail a030308_tabf) [[]] where

   f (bs:_:bss) pss = y : f bss pss' where

     y = foldr (\d v -> 2 * v + d) 0 ys

     (ys:_) = dropWhile (\ps -> not $ and $ zipWith (<=) ps bs) pss'

     pss' = if bs /= reverse bs then pss else bs : pss

-- Reinhard Zumkeller, Dec 11 2015

CROSSREFS

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

Cf. A007088, A030308.

Sequence in context: A196189 A206543 A274988 * A265527 A217250 A213923

Adjacent sequences:  A265506 A265507 A265508 * A265510 A265511 A265512

KEYWORD

nonn,base,look

AUTHOR

N. J. A. Sloane, Dec 09 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 24 23:01 EDT 2019. Contains 326314 sequences. (Running on oeis4.)