A265525 a(n) = largest base-10 palindrome m <= n such that every base-10 digit of m is <= the corresponding digit of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 11, 11, 11, 11, 11, 11, 11, 11, 0, 11, 22, 22, 22, 22, 22, 22, 22, 22, 0, 11, 22, 33, 33, 33, 33, 33, 33, 33, 0, 11, 22, 33, 44, 44, 44, 44, 44, 44, 0, 11, 22, 33, 44, 55, 55, 55, 55, 55, 0, 11, 22, 33, 44, 55, 66, 66, 66, 66, 0, 11, 22, 33, 44, 55, 66, 77, 77, 77, 0, 11, 22, 33

Offset: 0

Author

N. J. A. Sloane, Dec 09 2015

Keywords

• nonn
• base
• look

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..9999

Crossrefs

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

Cf. A002113, A031298, A265558.

Programs

Haskell

a265525 n = a265525_list !! n
a265525_list = f a031298_tabf [[]] where
   f (ds:dss) pss = y : f dss pss' where
     y = foldr (\d v -> 10 * v + d) 0 ys
     (ys:_) = dropWhile (\ps -> not $ and $ zipWith (<=) ps ds) pss'
     pss' = if ds /= reverse ds then pss else ds : pss
-- Reinhard Zumkeller, Dec 11 2015

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:=10; [seq(under10(n),n=0..144)]; # Gives A265525