A265559 - OEIS

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A265559

Smallest base-2 palindrome m >= n, written in base 2.

0, 1, 11, 11, 101, 101, 111, 111, 1001, 1001, 1111, 1111, 1111, 1111, 1111, 1111, 10001, 10001, 10101, 10101, 10101, 10101, 11011, 11011, 11011, 11011, 11011, 11011, 11111, 11111, 11111, 11111, 100001, 100001, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 101101, 110011

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..46.

MAPLE

ispal:= proc(n) global b; # test if n is base-b pallindrome

local L, Ln, i;

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

Ln:= nops(L);

for i from 1 to floor(Ln/2) do

if L[i] <> L[Ln+1-i] then return(false); fi;

od:

return(true);

end proc;

# find min pal >= n, write in base 10

big10:=proc(n) global b;

local t1, t2, i, m, sw1, L1;

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

L1:=nops(t1);

for m from n to 10*n do

if ispal(m) then return(m); fi;

od;

lprint("no solution in big10 for n = ", n);

end proc;

# find min pal >= n, write in base 10

bigb:=proc(n) global b;

local t1, t2, i, m, mb, sw1, L1;

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

L1:=nops(t1);

for m from n to 10*n do

if ispal(m) then t2:=convert(m, base, b); mb:=add(t2[i]*10^(i-1), i=1..nops(t2)); return(mb); fi;

od;

lprint("no solution in big10 for n = ", n);

end proc;

b:=2;

[seq(big10(n), n=0..144)]; # A206914

[seq(bigb(n), n=0..144)]; # A265559

MATHEMATICA

b2pal[n_]:=Module[{m=n}, While[IntegerDigits[m, 2]!=Reverse[IntegerDigits[m, 2]], m++]; FromDigits[ IntegerDigits[m, 2]]]; Array[b2pal, 50, 0] (* Harvey P. Dale, Feb 25 2024 *)

CROSSREFS

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

See A206914 for the values of m written in base 10.

Sequence in context: A088761 A215256 A265526 * A265543 A062128 A286618

Adjacent sequences: A265556 A265557 A265558 * A265560 A265561 A265562

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Dec 10 2015

STATUS

approved