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 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

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